Exhibit 5.1

		609 Main Street Houston, TX 77002 United States +1 713 836 3600 www.kirkland.com		Facsimile: +1 713 836 3601

November 15, 2024

NET Power Inc.

320 Roney Street, Suite 200

Durham, North Carolina 27701

Ladies and Gentlemen:

We are issuing this opinion in our capacity as special counsel to NET Power Inc. (the “Company”), in connection with the registration under the Securities Act of 1933, as amended (the “Act”), on a Registration Statement on Form S-3 to be filed with the Securities and Exchange Commission (the “Commission”) on or about the date hereof (the “Registration Statement”) of (a) the proposed issuance and sale, from time to time, by the Company, together or separately, of up to $750.0 million in the aggregate of (i) shares (the “Primary Common Shares”) of the Company’s Class A common stock, par value $0.0001 per share (“Class A Common Stock”), (ii) shares of the Company’s preferred stock, par value $0.0001 per share (“Preferred Stock”), (iii) warrants to purchase shares of Class A Common Stock or Preferred Stock (“Warrants”), (iv) rights to purchase shares of Class A Common Stock, Preferred Stock, Warrants or Units (as defined below) (“Rights”), and (v) units consisting of one or more of the foregoing securities listed in this clause (a) or any combination thereof (“Units” and, together with the Primary Common Shares, Preferred Stock, Warrants and Rights, the “Primary Securities”), and (b) the proposed resale, from time to time, by the selling stockholder (the “Selling Stockholder”) named in the Prospectus (as defined below) of up to 2,806,243 shares of Class A Common Stock (the “Selling Stockholder Securities”).

The Primary Securities and the Selling Stockholder Securities are collectively referred to herein as the “Securities.” The Securities are to be sold from time to time pursuant to the Registration Statement and will be offered on terms set forth in the Registration Statement and in the prospectus contained therein (the “Prospectus”) and any supplements to such prospectus (each, a “Prospectus Supplement”).

Each series of Warrants will be issued under a warrant agreement (each, a “Warrant Agreement”), to be filed in an amendment to the Registration Statement or incorporated by reference into the Registration Statement pursuant to a Current Report on Form 8-K of the Company and to be executed by the Company and a bank or trust company, as warrant agent, in each case prior to the issuance of such Warrants. Each series of Rights will be issued under a separate rights agreement (each, a “Rights Agreement”), to be filed in an amendment to the Registration Statement or incorporated by reference into the Registration Statement pursuant to a Current Report on Form 8-K of the Company and to be entered into between the Company and a bank or trust company, as rights agent, in each case prior to the issuance of such Rights.

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NET Power Inc.

November 15, 2024

Page 2

The applicable Prospectus Supplement with respect to the Securities offered will set forth the terms of the offering of such Securities, including the name or names of any underwriters, dealers or agents, the purchase price of such Securities and the proceeds to the Company or the Selling Stockholder from such sale, any underwriting discounts and other items constituting underwriters’ compensation, any public offering price and any discounts, commissions or concessions allowed or reallowed or paid to dealers, and any bidding or auction process. If underwriters are used in an offering of Securities registered by the Registration Statement, the Registration Statement anticipates that the Company or the Selling Stockholder will sell such Securities pursuant to the terms of an underwriting agreement to be executed between the Company, the Selling Stockholder (if applicable) and underwriters that will be identified in the applicable Prospectus Supplement. We have assumed for purposes of this letter that the terms of the Underwriting Agreement will fall within the scope of the authorization adopted by the Company’s board of directors (the “Board”) and will receive the approvals required by that Board authorization. The term “Underwriting Agreement” is used in this letter to mean an underwriting agreement in the form in which it will be actually executed by the Company, the Selling Stockholder (if applicable) and the underwriters with respect to a particular underwritten offering of Securities registered by the Registration Statement. We have also assumed for purposes of this letter that the terms of any other agreement providing for the sale of Securities registered by the Registration Statement (other than by means of an underwritten offering), including a distribution agreement to be filed prior to a particular offering of Securities registered by the Registration Statement in an amendment to the Registration Statement or incorporated by reference into the Registration Statement pursuant to a Current Report on Form 8-K of the Company, to be executed by the Company, the Selling Stockholder (if applicable) and an appropriate party or parties that will be identified in the applicable Prospectus Supplement, will fall within the scope of the authorization adopted by the Board and will receive the approvals required by that Board authorization. The term “Other Agreement” is used in this letter to mean an agreement providing for the sale of Securities registered by the Registration Statement (other than by means of an underwritten offering) in the form in which it will be actually executed by the Company, the Selling Stockholder (if applicable) and the appropriate party or parties with respect to a particular offering or offerings of Securities registered by the Registration Statement. The term “Agreement” is used in this letter to mean either an Underwriting Agreement or an Other Agreement. The terms “Registered Primary Common Shares,” “Registered Preferred Stock,” “Registered Warrants,” “Registered Rights” and “Registered Units” are used in this letter to mean, respectively, the Primary Common Shares, Preferred Stock, Warrants, Rights and Units that are registered under the Registration Statement as initially filed and are sold by the Company under an Agreement.

For purposes of this letter, we have examined originals, or copies certified or otherwise identified to our satisfaction, of such documents, corporate records and other instruments as we have deemed necessary for the purpose of this opinion, including (i) the corporate and organizational documents of the Company, (ii) minutes and records of the corporate proceedings of the Company with respect to the Registration Statement and the Securities and (iii) the Registration Statement and the exhibits thereto.

For purposes of this letter, we have assumed the authenticity of all documents submitted to us as originals, the conformity to the originals of all documents submitted to us as copies and the authenticity of the originals submitted to us as copies. We have also assumed the genuineness of the signatures of persons signing all documents in connection with which this opinion is rendered, the authority of such persons signing on behalf of the parties thereto other than the Company, and the due authorization, execution and delivery of all documents by the parties thereto other than the Company. As to any facts material to the opinions expressed herein which we have not independently established or verified, we have relied upon statements and representations of officers and other representatives of the Company and others.

Subject to the assumptions, qualifications and limitations identified in this letter, we advise you that in our opinion:

(1) Registered Primary Common Shares, when issued, will be validly issued, fully paid and non-assessable when, as and if (i) the Registration Statement shall have become effective pursuant to the provisions of the Act, (ii) appropriate corporate action shall have been taken by the Company to authorize the issuance and sale of such Registered Primary Common Shares, (iii) a Prospectus Supplement or Prospectus Supplements with respect to the Registered Primary Common Shares shall have been filed (or transmitted for filing) with the Commission pursuant to Rule 424(b) of the Act and any exhibits necessary under the rules and regulations of the Commission shall have been filed with the Commission in an amendment to the Registration Statement or incorporated by reference into the Registration Statement pursuant to a Current Report on Form 8-K of the Company filed with the Commission, (iv) any legally required consents, approvals, authorizations and other orders of the Commission and any other regulatory authorities shall have been obtained and (v) appropriate certificates representing the Registered Primary Common Shares are duly executed, countersigned by the Company’s transfer agent/registrar, registered and delivered against payment of the agreed consideration therefor (which shall be in an amount at least equal to the par value of the shares being issued and sold) in accordance with the applicable Agreement.

NET Power Inc.

November 15, 2024

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(2) Shares of Registered Preferred Stock, when issued, will be validly issued, fully paid and non-assessable when, as and if (i) the Registration Statement shall have become effective pursuant to the provisions of the Act, (ii) appropriate corporate action shall have been taken by the Company to establish the terms of such Registered Preferred Stock and to authorize the issuance and sale of such shares of Registered Preferred Stock, (iii) a Prospectus Supplement or Prospectus Supplements with respect to the shares of Registered Preferred Stock shall have been filed (or transmitted for filing) with the Commission pursuant to Rule 424(b) of the Act and any exhibits necessary under the rules and regulations of the Commission shall have been filed with the Commission in an amendment to the Registration Statement or incorporated by reference into the Registration Statement pursuant to a Current Report on Form 8-K of the Company filed with the Commission, (iv) any legally required consents, approvals, authorizations and other orders of the Commission and any other regulatory authorities shall have been obtained and (v) appropriate certificates representing the shares of Registered Preferred Stock are duly executed, countersigned by the Company’s transfer agent/registrar, registered and delivered against payment of the agreed consideration therefor (which shall be in an amount at least equal to the par value of the shares being issued and sold) in accordance with the applicable Agreement.

(3) Registered Warrants of each series, when issued, will be binding obligations of the Company, enforceable against the Company in accordance with their terms when, as and if (i) the Registration Statement shall have become effective pursuant to the provisions of the Act, (ii) appropriate corporate action shall have been taken by the Company to establish the terms of such Registered Warrants (which shall provide that the exercise price of such Warrants will consist of legal consideration in excess of the par value of the underlying shares of Class A Common Stock and/or Preferred Stock) and, if applicable, the terms of the Preferred Stock such Registered Warrants include and to authorize the form, terms, execution and delivery of a Warrant Agreement for such series of Registered Warrants, including a form of certificate evidencing such series of Registered Warrants (and such Warrant Agreement shall have been duly executed and delivered by the Company and the warrant agent or agents thereunder), (iii) a Prospectus Supplement or Prospectus Supplements with respect to such series of Registered Warrants shall have been filed (or transmitted for filing) with the Commission pursuant to Rule 424(b) of the Act and any exhibits necessary under the rules and regulations of the Commission, including such Warrant Agreement, shall have been filed with the Commission in an amendment to the Registration Statement or incorporated by reference into the Registration Statement pursuant to a Current Report on Form 8-K of the Company filed with the Commission, (iv) any legally required consents, approvals, authorizations and other orders of the Commission and any other regulatory authorities shall have been obtained, and (v) Registered Warrants of such series are duly executed, attested and issued by duly authorized officers of the Company, countersigned by the applicable warrant agent and delivered to the purchasers thereof against payment of the agreed consideration therefor in the manner provided for in the Registration Statement, any applicable Prospectus Supplements, such Warrant Agreement, the applicable Agreement and such corporate action.

(4) Registered Rights of each series, when issued, will be binding obligations of the Company, enforceable against the Company in accordance with their terms when, as and if (i) the Registration Statement shall have become effective pursuant to the provisions of the Act, (ii) appropriate corporate action shall have been taken by the Company to establish the terms of such Registered Rights (which, in the case of Rights to purchase shares of Class A Common Stock and/or Preferred Stock, shall provide that the exercise price of such Rights will consist of legal consideration in excess of the par value of such shares) and the terms of the Securities such Registered Rights include and to authorize the form, terms, execution and delivery of a Rights Agreement for such series of Registered Rights, including a form of certificate evidencing such series of Registered Rights (and such Rights Agreement shall have been duly executed and delivered by the Company and the rights agent or agents thereunder), (iii) a Prospectus Supplement or Prospectus Supplements with respect to such series of Registered Rights shall have been filed (or transmitted for filing) with the Commission pursuant to Rule 424(b) of the Act and any exhibits necessary under the rules and regulations of the Commission, including such Rights Agreement, shall have been filed with the Commission in an amendment to the Registration Statement or incorporated by reference into the Registration Statement pursuant to a Current Report on Form 8-K of the Company filed with the Commission, (iv) any legally required consents, approvals, authorizations and other orders of the Commission and any other regulatory authorities shall have been obtained, and (v) Registered Rights of such series are duly executed, attested and issued by duly authorized officers of the Company, countersigned by the applicable rights agent and delivered to the purchasers thereof against payment of the agreed consideration therefor in the manner provided for in the Registration Statement, any applicable Prospectus Supplements, such Rights Agreement, the applicable Agreement and such corporate action.

NET Power Inc.

November 15, 2024

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(5) Registered Units of each series, when issued, will be binding obligations of the Company enforceable against the Company in accordance with their terms, any shares of Class A Common Stock or Preferred Stock forming a part of such Registered Units will be validly issued, fully paid and non-assessable when such Registered Units are issued, and any Warrants or Rights forming a part of such Registered Units will be binding obligations of the Company enforceable against the Company in accordance with their terms when such Registered Units are issued, in each case when, as and if (i) the Registration Statement shall have become effective pursuant to the provisions of the Act, (ii) appropriate corporate action shall have been taken by the Company to establish the terms of such Registered Units and the terms of the Securities such Registered Units include, to authorize the issuance and sale of such Registered Units and, if applicable, to authorize the form, terms, execution and delivery of a units agreement (and such units agreement shall have been duly executed and delivered by the Company and the counterparty thereto), (iii) a Prospectus Supplement or Prospectus Supplements with respect to such series of Registered Units shall have been filed (or transmitted for filing) with the Commission pursuant to Rule 424(b) of the Act and any exhibits necessary under the rules and regulations of the Commission, including a unit agreement or other instrument establishing such Registered Units or defining the rights of holders of such Registered Units, shall have been filed with the Commission in an amendment to the Registration Statement or incorporated by reference into the Registration Statement pursuant to a Current Report on Form 8-K of the Company filed with the Commission, (iv) any legally required consents, approvals, authorizations and other orders of the Commission and any other regulatory authorities shall have been obtained, and (v) Registered Units of such series are duly executed, attested and issued by duly authorized officers of the Company, countersigned by the applicable transfer agent and delivered to the purchasers thereof against payment of the agreed consideration therefor (which, in the case of Registered Units consisting of one or more shares of Class A Common Stock or Preferred Stock, shall be in an amount at least equal to the par value of such shares) in the manner provided for in the Registration Statement, any applicable Prospectus Supplements, such Unit Agreement, the applicable Agreement and such corporate action.

(6) The Selling Stockholder Securities have been validly issued and are fully paid and non-assessable.

Our advice on every legal issue addressed in this letter is based exclusively on the internal law of New York and the General Corporation Law of the State of Delaware (under which the Company is incorporated).

Our opinions expressed above are subject to the qualifications that we express no opinion as to the applicability of, compliance with, or effect of (i) any bankruptcy, insolvency, reorganization, fraudulent transfer, fraudulent conveyance, moratorium or other similar law or judicially developed doctrine in this area (such as substantive consolidation or equitable subordination) affecting the enforcement of creditors’ rights generally, (ii) general principles of equity (regardless of whether enforcement is considered in a proceeding in equity or at law), (iii) an implied covenant of good faith and fair dealing, (iv) public policy considerations which may limit the rights of parties to obtain certain remedies, (v) any requirement that a claim with respect to any security denominated in other than U.S. dollars (or a judgment denominated in other than U.S. dollars in respect of such claim) be converted into U.S. dollars at a rate of exchange prevailing on a date determined in accordance with applicable law, (vi) governmental authority to limit, delay or prohibit the making of payments outside of the United States or in a foreign currency or currency unit and (vii) any laws except the laws of the State of New York and the General Corporation Law of the State of Delaware. We advise you that issues addressed by this letter may be governed in whole or in part by other laws, but we express no opinion as to whether any relevant difference exists between the laws upon which our opinions are based and any other laws which may actually govern.

For purposes of rendering our opinions expressed above, we have assumed that (i) the Registration Statement remains effective during the offer and sale of the particular Securities, (ii) the terms of any Warrant Agreement, Rights Agreement and any unit agreement or other instrument establishing Registered Units or defining the rights of holders of such Registered Units, each as applicable to the particular Securities, will be governed by New York law and will be consistent with the description of the terms of such agreement set forth in the Registration Statement and in the Prospectus (including any Prospectus Supplement), and (iii) at the time of the issuance, sale and delivery of each such Security (x) the authorization of such Security by the Company will not have been modified or rescinded, and there will not have occurred any change in law affecting the validity, legally binding character or enforceability of such Security and (y) the issuance, sale and delivery of such Security, the terms of such Security and compliance by the Company with the terms of such Security will not violate any applicable law, any agreement or instrument then binding upon the Company or any restriction imposed by any court or governmental body having jurisdiction over the Company.

We do not find it necessary for the purposes of this opinion, and accordingly we do not purport to cover herein, the application of the securities or “Blue Sky” laws of the various states to the issuance or sale of the Securities.

NET Power Inc.

November 15, 2024

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This opinion is limited to the specific issues addressed herein, and no opinion may be inferred or implied beyond that expressly stated herein. We assume no obligation to revise or supplement this opinion should the present laws of the State of New York or the General Corporation Law of the State of Delaware be changed by legislative action, judicial decision or otherwise.

This opinion is furnished to you in connection with the filing of the Registration Statement and is not to be used, circulated, quoted or otherwise relied upon for any other purposes.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement. We also consent to the reference to our firm under the heading “Legal Matters” in the Prospectus. In giving this consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act of the rules and regulations of the Commission.