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One mole of a gas obeying the equation of state $P(V-b)=R T$ is made to expand from a state with coordinates $\left(P_{1}, V_{1}\right)$ to a state with $\left(P_{2}, V_{2}\right)$ along a process that is depicted by a straight line on a $P-V$ diagram. Then, the work done is given by
Two cylinders contain same amount of ideal monatomic gas. Same amount of heat is given to two cylinders. If temperature rise in cylinder $A$ is $T_0$ then temperature rise in cylinder $B$ will be .........
$Assertion :$ In adiabatic compression, the internal energy and temperature of the system get decreased.
$Reason :$ The adiabatic compression is a slow process.
A gas is enclosed in a cylinder with a movable frictionless piston. Its initikl thermodynamic state at pressure $P_i=10^5 \mathrm{~Pa}$ and volume $V_i=10^{-3} \mathrm{~m}^3$ chanıes to i final state at $P_f=(1 / 32) \times 10^5 \mathrm{~Pa}$ and $V_f=8 \times 10^{-3} \mathrm{~m}^3$ in an adiabatic quasi-static process, such that $P^3 V^5=$ constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at $P$, followed by an isochoric (isovolumetric) process at volume $V_f$. The amount of heat supplied to the system in the two-step process is approximately
One mole of a perfect gas in a cylinder fitted with a piston has a pressure $P,$ volume $V$ and temperature $T.$ If the temperature is increased by $1 \,K$ keeping pressure constant, the increase in volume is
For two different gases $X$ and $Y$, having degrees of freedom $f_1$ and $f_2$ and molar heat capacities at constant volume $C_{V1}$ and $C_{V2}$ respectively, the ln $P$ versus ln $V$ graph is plotted for adiabatic process, as shown
The temperature inside and outside of refrigerator are $260\, K$ and $315\, K$ respectively. Assuming that the refrigerator cycle is reversible, calculate the heat delivered to surroundings for every joule of work done.