Under isothermal condition, the pressure of a gas is given by $P = aV ^{-3}$, where $a$ is a constant and $V$ is the volume of the gas. The bulk modulus at constant temperature is equal to $..........\,P$
JEE MAIN 2023, Diffcult
Download our app for free and get started
$B =-\frac{ dP }{ dv / v }$
$Pv ^3= a$
Differentiating w.r.t to pressure
$v^3+P 3 v^2 \frac{d v}{d P}=0$
$v=-3 \frac{P d v}{d P}=0$
$v=-3 \frac{P d v}{d P}$
$\frac{d P . v}{d v}=-3 P$
$B=-\left(\frac{d P v}{d v}\right)=-(-3 P)=3 P$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1$\Delta U + \Delta W = 0$ is valid forView Solution
- 2When $1\, kg$ of ice at $0^o C$ melts to water at $0^o C,$ the resulting change in its entropy, taking latent heat of ice to be $80\, cal/gm,$ is ...... $cal/K$View Solution
- 3$300 \,cal$. of heat is given to a heat engine and it rejects $225 \,cal$. of heat. If source temperature is $227^{\circ} C$, then the temperature of sink will be____${ }^{\circ} C$.View Solution
- 4The heat energy required to raise the temperature of $5\,moles$ of an ideal gas to $5\,K$ at constant pressure is $600\,J$ . How much heat (in $J$ ) is required to raise the same mass of the same gas to $5\,K$ at constant volume ? (Take $R = 8.3\,J/mole-^oK$ )View Solution
- 5In the $P-V$ diagram shown, the gas does $5\, J$ of work in isothermal process $ab$ and $4\,J$ in adiabatic process $bc$. .... $J$ will be the change in internal energy of the gas in straight path $c$ to $a$ ?View Solution
- 6Thermodynamic processes are indicated in the following diagram.View Solution
Match the following
$\begin{array}{|l|l|} \hline Column\,\,-\,\,1 & Column\,\,-\,\,2 \\ \hline P\,:\,Process\,\,-\,\,I & \,\,A\,\,:\,\,Adiabatic \\ \hline Q\,:\,Process\,\,-\,\,II & \,\,B\,\,:\,\,Isobaric \\ \hline R\,:\,Process\,\,-\,\,III & \,\,C\,\,:\,\,Isochoric \\ \hline S\,:\,Process\,\,-\,\,IV & \,\,D\,\,:\,\,Isothermal \\ \hline \end{array}$
- 7View SolutionWork done in the cyclic process shown in figure is ...........
- 8Gas obey $P^2V =$ constant. The initial temperature and volume are $T_0$ and $V_0$. If gas expands to volume $2V_0$, the final temp isView Solution
- 9A Carnot's engine working between $400\, K$ and $800\, K$ has a work output of $1200\, J$ per cycle. The amount of heat energy supplied to the engine from the source in each cycle is ........... $J$View Solution
- 10The first law of thermodynamics can be written as $ \Delta U = \Delta Q + \Delta W$ for an ideal gas. Which of the following statements is correct?View Solution