If 32 gm of \(O_2\)${\mathrm{}}_{}$ at \(27^{\circ}\mathrm{C}\) is mixed with 64 gm of \(O_2\)${\mathrm{}}_{}$ at \(327^{\circ}\mathrm{C}\) in an adiabatic vessel, then the final temperature of the mixture will be:
1. \(200^{\circ}\mathrm{C}\)
2. \(227^{\circ}\mathrm{C}\)
3. \(314.5^{\circ}\mathrm{C}\)
4. \(235.5^{\circ}\mathrm{C}\)$\mathrm{}$

If $W_1$ is the work done in compressing an ideal gas from a given initial state through a certain volume isothermally and $W_2$ is the work done in compressing the same gas from the same initial state through the same volume adiabatically, then:

1. $W_1=W_2$

2. $W_1<W_2$

3. $W_1>W_2$

4. $W_1=2W_2$

Temperature is defined by

1.  First Law of thermodynamics

2.  Second Law of thermodynamics

3.  Third Law of  thermodynamics

4.  Zeroth Law of  thermodynamics

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.  $\mathrm{\gamma } - 1$

For the indicator diagram given below, which of the following is not correct?

A sink, that is, the system where heat is rejected, is essential for the conversion of heat into work. From which law does the above inference follow?
1. Zeroth
2. First
3. Second
4. Third

The ratio of the relative rise in pressure for adiabatic compression to that for isothermal compression is

1. $\gamma$

2. $\frac{1}{\gamma }$

3. 1-$\gamma$

4. $\frac{1}{1-\gamma }$

A given mass of gas expands from state \(A\) to state \(B\) by three paths \(1, 2~\text{and}~3\), as shown in the figure. If \(W_1, W_2~\text{and}~W_3\) respectively be the work done by the gas along the three paths, then:

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