The ratio of the specific heats \(\frac{{C}_{{P}}}{{C}_{{V}}}=\gamma\) in terms of degrees of freedom(\(n\)) is given by:
1. | \(\left(1+\frac{1}{n}\right )\) | 2. | \(\left(1+\frac{n}{3}\right)\) |
3. | \(\left(1+\frac{2}{n}\right)\) | 4. | \(\left(1+\frac{n}{2}\right)\) |
1. | \(379\) J | 2. | \(357\) J |
3. | \(457\) J | 4. | \(374\) J |
If \(C_p\) and \(C_v\) denote the specific heats (per unit mass) of an ideal gas of molecular weight \(M\) (where \(R\) is the molar gas constant), the correct relation is:
1. \(C_p-C_v=R\)
2. \(C_p-C_v=\frac{R}{M}\)
3. \(C_p-C_v=MR\)
4. \(C_p-C_v=\frac{R}{M^2}\)
The amount of heat energy required to raise the temperature of \(1\) g of Helium at NTP, from \({T_1}\) K to \({T_2}\) K is:
1. \(\frac{3}{2}N_ak_B(T_2-T_1)\)
2. \(\frac{3}{4}N_ak_B(T_2-T_1)\)
3. \(\frac{3}{4}N_ak_B\frac{T_2}{T_1}\)
4. \(\frac{3}{8}N_ak_B(T_2-T_1)\)
For hydrogen gas \(C_P-C_V=a\) and for oxygen gas \(C_P-C_V=b\) where molar specific heats are given. So the relation between \(a\) and \(b\) is given by: (where \(C_p\) and \(C_V\) in J mol-1 K-1)
1. \(a=16b\)
2. \(b=16a\)
3. \(a=4b\)
4. \(a=b\)