An ideal gas follows a process described by $p V^2=C$ from $\left(p_1, V_1, T_1\right)$ to $\left(p_2, V_2, T_2\right)$ and $C$ is a constant. Then,
KVPY 2014, Medium
Download our app for free and get started
(b)
$p V^2=C \Rightarrow\left(\frac{n R T}{V}\right) \cdot V^2=C$
$[\therefore$ for an ideal gas, $p V=n R T]$
$\Rightarrow \quad T V=\frac{C}{n R}=$ a constant
$\therefore \quad T \propto-\frac{1}{V}$
So, if $V_2 > V_1$, then $T_2 < T_1$.
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
- 1One mole of an ideal gas at an initial temperature of $T\, K$ does $6 R$ joules of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $5/3$, the final temperature of gas will beView Solution
- 2View SolutionIn an isothermal process the volume of an ideal gas is halved. One can say that
- 3The efficiency of Carnot's engine operating between reservoirs, maintained at temperatures ${27^o}C$ and $ - {123^o}C,$ is ...... $\%$View Solution
- 4A reversible cyclic process for an ideal gas is shown below. Here, $P, V$, and $T$ are pressure, volume and temperature, respectively. The thermodynamic parameters $q, w, H$ and $U$ are heat, work, enthalpy and internal energy, respectively.View Solution
(image)
The correct option ($s$) is (are)
$(A)$ $q_{A C}=\Delta U_{B C}$ and $W_{A B}=P_2\left(V_2-V_1\right)$
$(B)$ $\mathrm{W}_{\mathrm{BC}}=\mathrm{P}_2\left(\mathrm{~V}_2-\mathrm{V}_1\right)$ and $\mathrm{q}_{\mathrm{BC}}=\mathrm{H}_{\mathrm{AC}}$
$(C)$ $\Delta \mathrm{H}_{\mathrm{CA}}<\Delta \mathrm{U}_{\mathrm{CA}}$ and $\mathrm{q}_{\mathrm{AC}}=\Delta \mathrm{U}_{\mathrm{BC}}$
$(D)$ $\mathrm{q}_{\mathrm{BC}}=\Delta \mathrm{H}_{\mathrm{AC}}$ and $\Delta \mathrm{H}_{\mathrm{CA}}>\Delta \mathrm{U}_{\mathrm{CA}}$
- 5Three processes form a thermodynamic cycle as shown on $P-V$ diagram for an ideal gas. Process $1 \rightarrow 2$ takes place at constant temperature $(300K$). Process $2 \rightarrow 3$ takes place at constant volume. During this process $40J$ of heat leaves the system. Process $3 \rightarrow 1$ is adiabatic and temperature $T_3$ is $275K$. Work done by the gas during the process $3 \rightarrow 1$ is ..... $J$View Solution
- 6View SolutionWhen an ideal triatomic non-linear gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is
- 7Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason $R$.View Solution
Assertion $A$ : If $dQ$ and $dW$ represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics $d Q=d U-d W$.
Reason $R :$ First law of thermodynamics is based on law of conservation of energy.
In the light of the above statements, choose the correct answer from the option given below :
- 8In an adiabatic process where in pressure is increased by $\frac{2}{3}\% $ if $\frac{{{C_p}}}{{{C_v}}} = \frac{3}{2},$ then the volume decreases by aboutView Solution
- 9Work done by $0.1$ mole of a gas at ${27^o}C$ to double its volume at constant pressure is ....... $cal$ ($R = 2 \,cal\, mol^{-1}$ $^oC^{-1}$)View Solution
- 10A motor-car tyre has a pressure of $2\, atm$ at $27\,^oC$. It suddenly burst's. If $\left( {\frac{{{C_p}}}{{{C_v}}}} \right) = 1.4$ for air, find the resulting temperatures (Given $4^{1/7} = 1.219$)View Solution