During a particular process, a monatomic ideal gas absorbs an amount of heat Q and performs work equal to Q/2 on its surroundings. Determine the molar heat capacity of the gas for this process.

Question

Quantrex Academy · Accepted Answer

Correct answer: B. 3R

According to the first law of thermodynamics:

Q = \Delta U + W

Given that the work done is

W = \dfrac{Q}{2}

:

Q = \Delta U + \dfrac{Q}{2}

\Delta U = \dfrac{Q}{2}

Using

\Delta U = n C_v \Delta T

and

Q = n C \Delta T

:

n C_v \Delta T = \dfrac{n C \Delta T}{2}

C = 2 C_v

For a monatomic ideal gas, the molar heat capacity at constant volume is

C_v = \dfrac{3}{2}R

.

C = 2 \left(\dfrac{3}{2}R\right) = 3R

During a particular process, a monatomic ideal gas absorbs an...

Options

Correct answer

Step-by-step solution

More from Specific Heat Capacities of Gases