Question 1 :
{tex} C _ { v } {/tex} and {tex} C _ { p } {/tex} denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then

Question 2 :
The figure shows the P-V plot of an ideal gas taken through a cycle {tex} A B C D A {/tex}. The part {tex} A B C {/tex} is a semi-circle and {tex} C D A {/tex} is half of an ellipse. Then,<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2becc3cb4340598d49bbbd"><br>

Question 3 :
Temperature of 1000 grams of nitrogen is raised from -20⁰C to 100⁰C at constant pressure. Given: specific heat at constant volume C_v = 5 cal/mole ⁰C and R = 2Cal/mole ⁰C<br>

Question 4 :
An ideal gas is taken from the state {tex} A {/tex} (pressure {tex} P {/tex}, volume {tex} V {/tex} ) to the state {tex} B {/tex} (pressure {tex} P / 2 {/tex}, volume {tex} 2 V {/tex} ) along a straight line path in the {tex} P - V {/tex} diagram. Select the correct statement (s) from the following:

Question 6 :
P-V diagram of a cyclic process ABCA is as shown in figure. Choose the correct statement (s): <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e8b20d560d51c030bee43c2' height='107' width='106' ><br>

Question 7 :
Heat is supplied to ice at a constant rate. Temperature variation with time is as shown is in fig. -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e8b20d4dc6c090247734dde' height='88' width='157' ><br>

Question 8 :
For the PV diagram shown , for path 1-2-3, 100 J of heat is given to the system and 40 J of work is done by the system. For path 1-4-3 the work done by system is 10 J. Then - <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e8b20d1dc6c090247734ddc' height='101' width='115' ><br>

Question 9 :
An ideal gas undergoes an expansion from a state with temperature T, and volume V₁ to V₂ through three different polytropic processes A, B and C as shown in the P-V diagram. If |&Delta;E_A|, |&Delta;E_B| and |&Delta;E_C| be the magnitude of changes in internal energy along the three paths respectively -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e8b20d3dc6c090247734ddd' height='93' width='121' ><br>

Question 10 :
An iron block of mass $2\;kg$, falls from a height of $10m$. After colliding with the ground it loses $25\%$ energy to surroundings and rest is gained as heat. Then find the temperature rise of the block. (Take sp. heat of iron $470\;J/kg^{\circ}C$)<br/>

Question 11 :
AB: isothermal (T_A= 300 K)<br>BC : Adiabatic (Work = 5 J)<br>CD : Constant pressure(5atm)<br>DE : Isothermal<br>EA : Adiabatic (Change in internal energy 8J) -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e8b20c160d51c030bee43af' height='116' width='174' ><br>

Question 12 :
An ideal gas undergoes an expansion from a state with temperature T, and volume V₁ to V₂ through three different polytropic processes A, B and C as shown in the P-V diagram. If |&Delta;E_A|, |&Delta;E_B| and |&Delta;E_C| be the magnitude of changes in internal energy along the three paths respectively -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e8b20d3dc6c090247734ddd' height='93' width='121' ><br>

Question 13 :
A gas is taken through a cyclic process. The change in internal energy along the path from c to a is - 160 J. Heat transferred along the path from a to b is 200 J and 40 J from path b to c. Then -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e8b20c4afa64601c3e36d16' height='108' width='145' ><br>

Question 14 :
A cylinder of mass $1$kg is given heat of $20000$J at atmospheric pressure. If initially temperature of cylinder is $20^o$C, find change in internal energy of the cylinder.<br>(Given that Specific heat capacity of cylinder $=400$J $kg^{-1}$ $^0C^{-1}$, Coefficient of volume expansion $=9\times 10^{-5}$ $^0C^{-1}$, Atmospheric pressure $=10^5$ $N/m^2$ and Density of cylinder $=9000$ $kg/m^3$).<br>

Question 15 :
Two moles of an ideal monoatomic gas, initially at pressure $P_1$ and volume $V_1$ undergo an adiabatic compression until its volume is $V_2$. Then the gas is given heat Q at constant volume $V_2$. Find the total work done by the gas, the total change in its internal energy and the final temperature of the gas.[Give your answers in terms of $P_1, V_1, V_2$Q and R].