A monoatomic gas is taken through a process T | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given the process equation: $TP^{-1/3} = 	ext{constant}$.Using the ideal gas law $PV = nRT$, we have $T \propto PV$, so $PV \cdot P^{-1/3} = 	ex

Vedclass · Accepted Answer

Its temperature will decrease

Vedclass · Answer

(C) Given the process equation: $TP^{-1/3} = 	ext{constant}$.Using the ideal gas law $PV = nRT$, we have $T \propto PV$, so $PV \cdot P^{-1/3} = 	ext{constant}$, which simplifies to $P^{2/3}V = 	ext{constant}$.Raising both sides to the power of $3/2$, we get $PV^{3/2} = 	ext{constant}$.This is a polytropic process $PV^x = 	ext{constant}$ where $x = 3/2$.For a monoatomic gas, the adiabatic index $\gamma = 5/3$.The molar heat capacity $C$ for a polytropic process is given by $C = \frac{R}{\gamma - 1} + \frac{R}{1 - x}$.Substituting the values: $C = \frac{R}{5/3 - 1} + \frac{R}{1 - 3/2} = \frac{R}{2/3} + \frac{R}{-1/2} = \frac{3R}{2} - 2R = -\frac{R}{2}$.Since the molar heat capacity $C$ is negative, from the relation $\Delta Q = nC\Delta T$, if heat is given to the gas $(\Delta Q > 0)$, then $\Delta T$ must be negative $(\Delta T Therefore, the temperature of the gas will decrease.

$A$ monoatomic gas is taken through a process $TP^{-1/3} = \text{constant}$. If heat is given to the gas, what happens to its temperature?

Similar Questions

For a certain process, the pressure of a diatomic gas varies according to the relation $P = aV^2$, where $a$ is a constant. What is the molar heat capacity of the gas for this process?

The $P-V$ diagram of a monoatomic gas is a straight line passing through the origin. The molar heat capacity of the gas in this process will be:

During an experiment,an ideal gas is found to obey an additional law $VP^2 = \text{constant}$. The gas is initially at temperature $T$ and volume $V$. When the gas expands to a volume $2V$,its temperature will be:

One mole of an ideal monoatomic gas expands along the polytropic process $PV^3 = \text{constant}$ from volume $V_1$ to $V_2$. The molar specific heat capacity for this process is given by $C = C_V + \frac{R}{1-n}$. The total heat absorbed during the process can be expressed as:

The variation of pressure $P$ with volume $V$ for an ideal diatomic gas is parabolic as shown in the figure. The molar specific heat of the gas during this process is

Vedclass Test Series

Exam Paper Generator

Online Exam Module