Question

We start with 5.00 moles of an ideal monatomic gas with an initial temperature of 129 ∘C. The gas expands and, in the process, absorbs an amount of heat equal to 1180 J and does an amount of work equal to 2160 J . What is the final temperature Tfinal of the gas? Use R = 8.3145 J/(mol⋅K) for the ideal gas constant.

Answer 1

The solution is in the attachment

Answer 2

The final temperature of an ideal monatomic gas with an initial temperature of 128°C. is 114.53°C.

From the first law of thermodynamics,

ΔU=Q - W

Where,

ΔU - change in internal energy

Q - energy absorbed

W - work

So,

ΔU = 1180 J - 2020 J

ΔU = -840 J

From ideal gas law

$\bold {\Delta U = \dfrac 32n R (T_2- T_1)}}\\\\\bold {T_ 2 = \dfrac {2\Delta U}{3nR} +T_1}$

Where, T2 is the final temperature,

n- moles of gas

R - gas constant

T1 - initial temperature,

Put the values in the equation

$\bold {T_ 2 = \dfrac {2\times -840\ J )}{3\times 5 \times 8.314\ J/mol.K} + 128^oC}\\\\\bold {T_2 = 114.53 ^oC}$

Therefore, the final temperature of an ideal monatomic gas with an initial temperature of 128°C. is 114.53°C.

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