A sample of water of mass \(m\) kg is heated slowly from an initial temperature \(T_1\) K to a final temperature \(T_2\) K, where \(T_2>T_1.\) If the specific heat capacity of water is constant and equal to \(1 ~\text{J kg}^{-1}\text{K}^{-1},\) the change in entropy of the water is:
1. \(0\)
2. \(m\ln\left(\dfrac{T_1}{T_2}\right)~\text{J K}^{-1}\)
3. \(m(T_2-T_1)~\text{J K}^{-1}\)
4. \(m\ln\left(\dfrac{T_2}{T_1}\right)~\text{J K}^{-1}\)

An isolated system consists of two compartments containing an ideal gas, separated by a removable partition. The initial entropies of the gases in the two compartments are \({S_1}\) and \({S_2},\) respectively, where \({S_1 > S_2.}\) What is the initial total entropy of the system before the partition is removed?
 1. \(S_1\text - S_2 \)
2. \(\dfrac{S_1}{S_2} \)
3. \(S_1 \times S_2 \)
4. \(S_1+S_2\)

A solid body has a constant heat capacity of \(1~\text{J K}^{-1}.\) It is heated from \(100~\text{K}\) to \(200~\text{K}\) in two different ways:
(i) By placing it successively in contact with \(2\) thermal reservoirs, each supplying the same amount of heat.
(ii) By placing it successively in contact with \(8\) thermal reservoirs, each supplying the same amount of heat.
The entropy changes of the body in cases (i) and (ii), respectively, are:
1. \(\ln2,~~4 \ln2 \)
2. \(\ln 2, ~~\ln 2 \)
3. \(\ln 2,~~2 \ln 2 \)
4. \(2 \ln 2,~~8 \ln 2\)