Exhibit 24.1

                                 POWER OF ATTORNEY

                                   October 13, 2021

      Know all by these presents, that the undersigned hereby constitutes and
appoints Rhett Bennett of Black Mountain Acquisition Corp. (the "Company"), and
with full power of substitution, the undersigned's true and lawful
attorney-in-fact to:

      1.     prepare, execute in the undersigned's name and on the undersigned's
behalf, and submit to the U.S. Securities and Exchange Commission (the "SEC") a
Form ID, including amendments thereto, and any other documents necessary or
appropriate to obtain codes and passwords enabling the undersigned to make
electronic filings with the SEC of reports required by Section 16(a) of the
Securities Exchange Act of 1934, as amended, or any rule or regulation of
the SEC;

      2.     execute for and on behalf of the undersigned with respect to the
Company, Schedules 13D and 13G and Forms 3, 4 and 5 in accordance with
Sections 13 and 16(a) of the Securities Exchange Act of 1934, as amended, and
the rules thereunder;

      3.     do and perform any and all acts for and on behalf of the
undersigned which may be necessary or desirable to complete and execute any such
Schedules 13D or 13G or Form 3, 4 or 5, complete and execute any amendment or
amendments thereto, and timely file such form with the SEC and any stock
exchange or similar authority; and

      4.     take any other action of any type whatsoever in connection with the
foregoing which, in the opinion of such attorney-in-fact, may be of benefit to,
in the best interest of, or legally required by, the undersigned, it being
understood that the documents executed by such attorney-in-fact on behalf of the
undersigned pursuant to this Power of Attorney shall be in such form and shall
contain such terms and conditions as such attorney-in-fact may approve in such
attorney-in-fact's discretion.

      The undersigned hereby grants to such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorney-in-fact, or such
attorney-in-fact's substitute, shall lawfully do or cause to be done by virtue
of this power of attorney and the rights and powers herein granted. The
undersigned acknowledges that the foregoing attorney-in-fact, in serving in such
capacity at the request of the undersigned, are not assuming, nor is the Company
assuming any of the undersigned's responsibilities to comply with Sections 13
and 16 of the Securities Exchange Act of 1934, as amended.

      This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4 and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorney-in-fact.

                            [Signature Page Follows]

      IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of the date written above.

                                                    /s/ Jacob Smith
                                                    Name: Jacob Smith

                        Signature Page to Power of Attorney