A calorimeter of water equivalent 20 g contains 180 g of water at $25°C$. 'm' grams of steam at $100°C$ is mixed and final temperature of the mixture is $31°C$. The value of 'm' is close to: (Latent heat of water = 540 cal g^-1, Specific heat of water = 1 cal g^{-1 o}C^-1)

1.   2
2.  2.6
3.  4
4.  3.2

If minimum possible work is done by a refrigerator in converting 100 grams of water at 0ºC to ice, what is the coefficient of performance if heat is released to the surroundings at temperature 27^ºC?

1. $\frac{27}{273}$

2. $\frac{273}{27}$

3. $\frac{7}{273}$

4. $\frac{273}{7}$

The specific heat of water = 4200 J kg^–1 K^–1 and the latent heat of ice = 3.15 × 10⁵ J kg^–1. 100 grams of ice at 0ºC is placed in 300 g of water at 25ºC. The amount of ice that will melt as the temperature of the water reaches 0ºC is close to (in grams):

1. 50

2. 100

3. 150

4. 200

A closed vessel contains \(0.1\) mole of a monatomic ideal gas at \(200~\text{K}\). If \(0.05\) mole of the same gas at \(500~\text{K}\) is added to it, the final equilibrium temperature (in \(\text{K}\)) of the gas in the vessel is:
1. \(100~\text{K}\)
2. \(200~\text{K}\)
3. \(300~\text{K}\)
4. \(400~\text{K}\)

Match the thermodynamic processes taking place in a system with the correct conditions. In the table, \(\Delta Q\) is the heat supplied, \(\Delta W\) is the work done and \(\Delta U\) is the change in internal energy of the system.