An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes $32$ times of its initial value. If the final pressure of gas is $128$ atmosphers, the value of $\gamma$ the gas is
JEE MAIN 2013, Medium
Download our app for free and get started
Volume of the gas
$v=\frac{m}{d}$ and
using $P V^{7}=$ constant
$\frac{P^{\prime}}{P}=\frac{V}{V^{\prime}}=\left(\frac{d^{\prime}}{d}\right)^{\gamma}$
$\alpha 128=(32)^{\gamma}$
$\gamma=\frac{7}{5}=1.4$
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
- 1A tyre filled with air $({27^o}C,$ and $2$ atm) bursts, then what is temperature of air ....... $^oC$ $(\gamma = 1.5)$View Solution
- 2An engine has an efficiency of $1/6.$ When the temperature of sink is reduced by $62^o C,$ its efficiency is doubled. Temperatures of the source is ....... $^oC$View Solution
- 3One mole of an ideal gas is contained with in a cylinder by a frictionless piston and is initially at temperature $T$. The pressure of the gas is kept constant while it is heated and its volume doubles. If $R$ is molar gas constant, the work done by the gas in increasing its volume isView Solution
- 4View SolutionWork done per mol in an isothermal change is
- 5In a heat engine, the temperature of the source and sink are $500\, K$ and $375\, K$. If the engine consumes $25\times10^5\, J$ per cycle, the work done per cycle isView Solution
- 6Following figure shows $P-T$ graph for four processes $A, B, C$ and $D$. Select the correct alternative.View Solution
- 7A thermodynamic process is the pressure and volumes corresponding to some points in the figure are, $P_A = 3 \times 10^4 Pa$, $V_A = 2 \times 10^{-3}\, m^3$, $P_B = 8 \times 10^4 Pa$, $V_D = 5 \times 10^{-3}\,m^3$. In process $AB, 600\, J$ of heat and in process $BC, 200\, J$ of heat is added to the system. The change in the internal energy in process $AC$ would be .... $J$View Solution
- 8Two moles of helium gas are taken over the cycle $ABCDA$, as shown in the $P-T$ diagram. The net work done on the gas in the cycle $ABCDA$ is ...... $R$View Solution
- 9When an ideal gas $(\gamma = 5/3$) is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external workView Solution
- 10View SolutionThe temperature of an ideal gas is kept constant as it expands. The gas does external work. During this process, the internal energy of the gas