In a thermodynamic process, helium gas obeys | vedclass

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

Question

(C) Given the process law: $T P^{-2/5} = 	ext{constant}$.Using the ideal gas equation $PV = nRT$, we have $P = \frac{nRT}{V}$.Substituting $P$ into t

Vedclass · Accepted Answer

Zero

Vedclass · Answer

(C) Given the process law: $T P^{-2/5} = 	ext{constant}$.Using the ideal gas equation $PV = nRT$, we have $P = \frac{nRT}{V}$.Substituting $P$ into the given equation: $T (\frac{nRT}{V})^{-2/5} = 	ext{constant}$.This simplifies to $T \cdot T^{-2/5} \cdot V^{2/5} = 	ext{constant}$, which gives $T^{3/5} V^{2/5} = 	ext{constant}$.Raising both sides to the power of $5/3$, we get $T V^{2/3} = 	ext{constant}$.Since $T \propto PV$, we have $(PV) V^{2/3} = 	ext{constant}$, which implies $P V^{5/3} = 	ext{constant}$.This is an adiabatic process with adiabatic index $\gamma = 5/3$ (for helium, a monoatomic gas).For an adiabatic process, the heat exchanged $Q = 0$.

In a thermodynamic process, helium gas obeys the law $TP^{-2/5} = \text{constant}$. The heat given to the gas when the temperature of $2$ moles of the gas is raised from $T$ to $4T$ ($R$ is the universal gas constant) is:

Similar Questions

An ideal gas undergoes an adiabatic process. If the pressure of the gas is reduced by $0.1 \%$, then the volume is changed by (Given $\gamma = \frac{C_p}{C_v} = \frac{5}{3}$) (in $\%$)

In an adiabatic expansion of a gas,

The amount of work done in an adiabatic expansion from temperature $T$ to ${T_1}$ is

$A$ monatomic gas at pressure $P_1$ and volume $V_1$ is compressed adiabatically to $1/8$ of its original volume. What is the final pressure of the gas in terms of $P_1$?

$A$ monatomic gas at a pressure of $100 \text{ kPa}$ expands adiabatically such that its final volume becomes $8$ times its initial volume. If the work done during the process is $180 \text{ J}$, then the initial volume of the gas is (in $\text{ cm}^3$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module