1st Law of Thermodynamics

Q. Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following : (a) What is the final pressure of the gas in A and B ? (b) What is the change in internal energy of the gas ? (c) What is the change in the temperature of the gas ? (d) Do the intermediate states of the system (before settling to the final equilibrium state) lie on its P-V-T surface ?

Q. 16 kg oxygen gas expands at stp isobarically to occupy double of its original volume. The work done during the process is nearly

Q. In changing the state of a gas adiabatically from an equilibrium state A to another equilibrium state B, an amount of work equal to 22.3 J is done on the system. If the gas is taken from state A to B via a process in which the net heat absorbed by the system is 9.35 cal, how much is the net work done by the system in the latter case ? (Take 1 cal = 4.19 J)

Q. a gas is filled in a container of volume V at cons†an t pressure and at 27 degree celsius temperature . find out the amount of gas that will escape out of the container if temperature rises to 37 degree celsius ?

Q. One mole of an ideal gas whose pressure changes with volume as P=αV where α is constant. The molar heat capacity of the gas is :- (1)R (2)2R (3)3R (4)4R

Q. The percentage change in the volume of the given mass of gas at cons†an t temperature is 50percent(increases). Calculate the percentage change in the pressure of the gas?

Q. 1. 32 gram of oxygen gas at temperature 27C is compressed adiabatically to 1/3 of its initial volume. Calculatethe change in internal energy. (y 1.5 for oxygen

Q. A vertical cylinder closed at both ends is fitted with a smooth piston dividing the volume into two parts each containing one mole of air. At the equilibrium temperature of 320 K, the upper and lower parts are in the ratio 4:1. The ratio will become 3:1 at atemperature of (a) 450 K (b) 228 K (c) 570 K(d) 420 K

Q. A gas is undergoing a cyclic process as shown in figure, where $P_0=2\text{bar}$ and $V_0=7{\text{m}}^3$. Find the workdone ($W$) by the gas and heat ($Q$) released by the gas in one cycle.

1. $44\times {10}^5\text{J}$, $-44\times {10}^5\text{J}$
2. $-44\times {10}^5\text{J}$, $44\times {10}^5\text{J}$
3. $88\times {10}^5\text{J}$, $44\times {10}^5\text{J}$
4. $-88\times {10}^5\text{J}$, $88\times {10}^5\text{J}$

Q. Four identical samples of an ideal gas are taken along the paths $A,B,C$ and $D$ from state $1$ to state $2$ as shown in the $PV$ indicator diagram. Let $Q,W$ and $\Delta U$ represent the heat supplied, work done and change in internal energy of the gas respectively. Choose the correct option among the following :

1. $Q_A-Q_D=W_A-W_D$
2. $Q_B-W_B>Q_C-W_C$
3. $W_A<W_B<W_C<W_D$
4. $Q_A<Q_B<Q_C<Q_D$

Q.

A system which exchanges both matter & energy with the surrounding is called a closed system.

1. True

2. False

Q. An ideal monoatomic gas is at pressure $P_0$ and volume $V_0$. It is taken to final volume $2V_0$ and final pressure $\frac{P_0}{2}$ in a process which is straight line on $P-V$ diagram.

1. Final temperature is greater than initial temperature
2. Internal energy increases
3. Work done by the gas is $+\frac{P_0{V}_0}{4}$
4. Heat is absorbed by the gas

Q. The internal energy of a gas is given by $U=(2PV+20)\text{J}$. It expands from $100{\text{cm}}^3$ to $200{\text{cm}}^3$ against a constant pressure of $200\text{kPa}$. Calculate the heat absorbed by the gas in the process.

1. $-60\text{J}$
2. $40\text{J}$
3. $-40\text{J}$
4. $60\text{J}$

Q. A sample of ideal gas at ${100}^{\circ }\text{C}$ and normal pressure $(1.03\times {10}^5{\text{Nm}}^{-2})$ absorbs $54\text{cal}$ of heat energy at constant pressure. If the volume of the gas increases by $167\text{cc}$, the change in internal energy of the sample is :

1. $+104.4\text{J}$
2. $+208.8\text{J}$
3. $-84.5\text{J}$
4. $-242.6\text{J}$

Q. 12. in an isothermal reaction of a gaseous sample the correct relation is a) w rev>w irrev b)w irrev> w rev c) q rev

Q. A gas is compressed at a constant pressure of $50{\text{N/m}}^2$ from a volume of $10{\text{m}}^3$ to a volume of $4{\text{m}}^3$. Heat of $100\text{J}$ is then added to the gas by heating it at constant volume. Its internal energy is

1. Decreased by $200\text{J}$
2. Increased by $200\text{J}$
3. Decreased by $400\text{J}$
4. Increased by $400\text{J}$

Q. An ideal gas undergoes a thermodynamic process in which the work done by the gas is the same as the increase in the internal energy of the gas. The molar heat capacity of the gas for the process is
(Given, $\gamma =1.5$ for the gas)

1. $4R$
2. $2R$
3. $3R$
4. $5R$

Q. 273 cm cube of an ideal gas is at 0 degree Celsius. It is heated at constant pressure to 100 degree Celsius. It will now occupy how much volume

Q.

Figure 17.5 shows the P - V diagram for a fixed mass of an ideal gas undergoing cyclic process ABCA.AB represents isothermal process. Which of the graphs shown in Fig. 17.6 represents the P - T diagram of the cyclic process ?

1. 
   

2. 
   

3. 
   

4. 
   

Q. An ideal gas undergoes a thermodynamic process in which the work done by the gas is the same as the increase in the internal energy of the gas. The molar heat capacity of the gas for the process is
(Given, $\gamma =1.5$ for the gas)

1. $4R$
2. $2R$
3. $3R$
4. $5R$

Q. 66.: An ideal gas at 27^° c is compressed adabatically to 8/27 of its original volume.The rise in temprature is (take gamma = 5/3) 1. 475^° C 2. 150^° C 3.275^° C 4.402^° C

Q. An isolated system is a system in which

1. there is no exchange of energy with the surrounding.
2. there is exchange of mass and energy with the surrounding.
3. there is no exchange of energy and mass with the surrounding.
4. there is no exchange of mass with the surrounding.

Q. Why slope directly proportional to inverse of heat capacity

Q. In the arrangement shown in figure, gas is thermally insulated. An ideal gas is filled in the cylinder having pressure $P_0(>$ atmospheric pressure $P_a)$. The spring of force constant $K$ is initially unstretched. The piston of mass $m$ and area $S$ is frictionless. In equilibrium, the piston rises up by distance $x_0$, then

1. final pressure of the gas is $P_0+\frac{K{x}_0}{S}+\frac{mg}{S}$
2. work done by the gas is $\frac{1}{2}K{x}_0^2+mg{x}_0$
3. decrease in internal energy of the gas is $\frac{1}{2}K{x}_0^2+mg{x}_0+P_{a}S{x}_0$
4. all of the above

Q. In a certain process, $400\text{cal}$ of heat is supplied to a system and at the same time $105\text{J}$ of mechanical work was done on the system. The increase in its internal energy is

1. $425\text{cal}$
2. $375\text{cal}$
3. $505\text{cal}$
4. $295\text{cal}$

Q. Four identical samples of an ideal gas are taken along the paths $A,B,C$ and $D$ from state $1$ to state $2$ as shown in the $PV$ indicator diagram. Let $Q,W$ and $\Delta U$ represent the heat supplied, work done and change in internal energy of the gas respectively. Choose the correct option among the following :

1. $Q_A-Q_D=W_A-W_D$
2. $Q_B-W_B>Q_C-W_C$
3. $W_A<W_B<W_C<W_D$
4. $Q_A<Q_B<Q_C<Q_D$

Q. Air in a cylinder is suddenly compressed by a piston which is then maintained at the same position. As time passes, pressure of the gas

1. Increases
2. Decreases
3. May increase or decrease depending on the nature of gas
4. Remain the same

Q.

Define the terms- Volume

Q. If the heat of $110\text{J}$ is added to a gaseous system and it acquires internal energy of $40\text{J}$, then the amount of internal work done is

1. $40\text{J}$
2. $70\text{J}$
3. $150\text{J}$
4. $110\text{J}$

Q. The $P-V$ diagram of a system undergoing thermodynamic transformation is shown in figure. The work done by the system and heat given to the system in going from $A\to B\to C$ is $30\text{J}$ and $40\text{J}$ respectively. The change in internal energy between $A$ and $C$ is

1. $70\text{J}$
2. $10\text{J}$
3. $-70\text{J}$
4. $-10\text{J}$