During an adiabatic process,if the pressure o | vedclass

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

Question

(C) For an adiabatic process,the relationship between pressure $P$ and temperature $T$ is given by $P^{1-\gamma} T^{\gamma} = 	ext{constant}$.Given t

Vedclass · Accepted Answer

$\frac{3}{2}$

Vedclass · Answer

(C) For an adiabatic process,the relationship between pressure $P$ and temperature $T$ is given by $P^{1-\gamma} T^{\gamma} = 	ext{constant}$.Given that $P \propto T^3$,we can write $P = k T^3$,which implies $P T^{-3} = 	ext{constant}$.Comparing this with the standard adiabatic relation $P^{1-\gamma} T^{\gamma} = 	ext{constant}$,we raise the given relation to a power $n$ such that the exponent of $T$ matches:$(P T^{-3})^n = P^n T^{-3n} = 	ext{constant}$.Equating the exponents of $T$ from $P^{1-\gamma} T^{\gamma}$ and $P^n T^{-3n}$,we have $\gamma = -3n$ and $1-\gamma = n$.Substituting $n = 1-\gamma$ into the first equation: $\gamma = -3(1-\gamma) = -3 + 3\gamma$.Rearranging gives $2\gamma = 3$,so $\gamma = \frac{3}{2}$.Thus,the ratio $\frac{C_p}{C_V} = \gamma = \frac{3}{2}$.

During an adiabatic process,if the pressure of a gas is found to be proportional to the cube of its absolute temperature,then the ratio of $\frac{C_p}{C_V}$ for the gas is:

Similar Questions

For an adiabatic compression of $1 \text{ kmol}$ of gas,$146 \text{ kJ}$ of work is done. During this process,the temperature of the gas increases by $7 \text{ °C}$. The gas is ........

$A$ litre of dry air at $STP$ expands adiabatically to a volume of $3$ litres. If $\gamma=1.40,$ the work done by air is $(3^{1.4}=4.6555)$. [Take air to be an ideal gas] (in $; J$)

We consider a thermodynamic system. If $\Delta U$ represents the increase in its internal energy and $W$ the work done by the system,which of the following statements is true?

An ideal gas undergoes a process $A \rightarrow B \rightarrow C \rightarrow A$ cycle. The process $A \rightarrow B$ is adiabatic. Calculate the work done in the process $A \rightarrow B$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module