A thermodynamic process for one mole of an id | vedclass

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

Question

(D) For a polytropic process, the equation is $PV^{x} = 	ext{constant}$.Given the process equation is $PV^{1/2} = 	ext{constant}$.Using the ideal ga

Vedclass · Accepted Answer

$\frac{1}{\sqrt{2}}$

Vedclass · Answer

(D) For a polytropic process, the equation is $PV^{x} = 	ext{constant}$.Given the process equation is $PV^{1/2} = 	ext{constant}$.Using the ideal gas equation $PV = nRT$, we can write $P = \frac{nRT}{V}$.Substituting this into the process equation:$\left(\frac{nRT}{V}ight) V^{1/2} = 	ext{constant}$$T V^{-1} V^{1/2} = 	ext{constant}$$T V^{-1/2} = 	ext{constant}$Thus, $T_{1} V_{1}^{-1/2} = T_{2} V_{2}^{-1/2}$.Rearranging for the ratio of temperatures:$\frac{T_{2}}{T_{1}} = \left(\frac{V_{2}}{V_{1}}ight)^{-1/2} = \left(\frac{V_{1}}{V_{2}}ight)^{1/2}$.Given $V_{2} = 2V_{1}$, we have $\frac{V_{1}}{V_{2}} = \frac{1}{2}$.Therefore, $\frac{T_{2}}{T_{1}} = \left(\frac{1}{2}ight)^{1/2} = \frac{1}{\sqrt{2}}$.Hence, the correct option is $D$.

$A$ thermodynamic process for one mole of an ideal gas is shown below on a $P-V$ diagram. If $V_{2} = 2V_{1}$, then the ratio of temperature $T_{2} / T_{1}$ is ...... .

Similar Questions

One mole of an ideal monoatomic gas at temperature $T_0$ expands slowly according to the law $P/V = \text{constant}$. If the final temperature is $2 T_0$, heat supplied to the gas is:

$A$ gas expands in such a way that its pressure and volume satisfy the condition $PV^2 = \text{constant}$. Then the temperature of the gas

An ideal gas expands in such a manner that its pressure and volume are related by the equation $PV^2 = \text{constant}$. During this process, the gas is

The specific heat of a gas in a polytropic process is given by

Work done to increase the temperature of one mole of an ideal gas by $30^{\circ} C$,if it is expanding under the condition $V \propto T^{2/3}$ is,$(R = 8.314 \ J/mol \cdot K)$ (in $J$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module