A system is taken from state A to state B along two different paths 1 and 2. If the heat absorbed and work done by the system along these two paths are $Q_1, Q_2 and W_1, W_2$ respectively, then

(1) $Q_1=Q_2$

(2) $W_1=W_2$

(3) $Q_1-W_1=Q_2-W_2$

(4) $Q_1+W_1=Q_2+W_2$

In a given process, dW = 0, dQ < 0, then for the gas:
1. Temperature increases
2. Volume decreases
3. Pressure decreases
4. Pressure increases

An ideal gas with adiabatic exponent y is heated at constant pressure and it absorbs Q heat. What fraction of this heat is used to perform external work?

1.  $\mathrm{\gamma }$

2.  $\frac{1}{\mathrm{\gamma }}$

3.  $1 - \frac{1}{\mathrm{\gamma }}$

4.  $\mathrm{\gamma } - 1$

Figure below shows two paths that may be taken by a gas to go from a state A to a state C. In process AB, 400 J of heat is added to the system and in process BC, 100 J of heat is added to the system. The heat absorbed by the system in the process AC will be-

(a) 380 J 
(b) 500 J
(c) 460 J
(d) 300 J

A thermodynamic system is taken through the cycle ABCD as shown in figure. Heat rejected by the gas during the cycle is 

(a)2 pV                                     (b)4 pV

(c)$\frac{1}{2}pV$                                    (d)pV