In a thermodynamic process, 2 , text{moles} o | vedclass

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

Question

(B) The given process is a polytropic process defined by $P \propto V^{-2}$, which can be written as $P V^2 = 	ext{constant}$.Comparing this with the

Vedclass · Accepted Answer

$-200$

Vedclass · Answer

(B) The given process is a polytropic process defined by $P \propto V^{-2}$, which can be written as $P V^2 = 	ext{constant}$.Comparing this with the general polytropic equation $P V^n = 	ext{constant}$, we get the polytropic index $n = 2$.The work done by an ideal gas in a polytropic process is given by the formula $W = \frac{\mu R (T_1 - T_2)}{n - 1}$, or equivalently $W = \frac{\mu R \Delta T}{1 - n}$.Given: number of moles $\mu = 2$, initial temperature $T_1 = 300 \, K$, final temperature $T_2 = 400 \, K$, and $n = 2$.Substituting these values into the formula:$W = \frac{2 	imes R 	imes (400 - 300)}{1 - 2}$$W = \frac{2 	imes R 	imes 100}{-1}$$W = -200 \, R$.Thus, the work done by the gas is $-200 \, R$.

In a thermodynamic process, $2 \, \text{moles}$ of a monatomic ideal gas obey $P \propto V^{-2}$. If the temperature of the gas increases from $300 \, K$ to $400 \, K$, find the work done by the gas in terms of $R$ (where $R$ is the universal gas constant).

Similar Questions

One mole of a monoatomic ideal gas is expanded by a process described by $p V^3 = C$,where $C$ is a constant. The heat capacity of the gas during the process is given by ($R$ is the gas constant).

In an $H_2$ gas process, $PV^2 = \text{constant}$. The ratio of work done by the gas to the change in its internal energy is:

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 $J$)

One mole of an ideal monoatomic gas at temperature $T_0$ expands slowly according to the law $P = kV$ ($k$ is a constant). If the final temperature is $2T_0$,the heat supplied to the gas is:

An ideal gas with heat capacity at constant volume $C_V$ undergoes a quasistatic process described by $p V^{\alpha} = \text{constant}$ in a $p-V$ diagram,where $\alpha$ is a constant. The heat capacity of the gas during this process is given by

Vedclass Test Series

Exam Paper Generator

Online Exam Module