A bowl filled with very hot water cools from $98^\circ\text{C}$ to $86^\circ\text{C}$ in 2 minutes when the room temperature is $22^\circ\text{C}$. How long it will take to cool from $75^\circ\text{C}$ to $69^\circ\text{C}$ ?

A Carnot engine with efficiency 50% takes heat from a source at 600 K. To increase the efficiency by 20%, keeping temperature of the sink same, the new temperature of the source will be

One gram of a liquid is converted to vapour at $3 \times 10^5$ Pa pressure. If 10% of the heat supplied is used for increasing the volume by $1600\ \text{cm}^3$ during this phase change, then the increase in internal energy in the process will be

The average transnational kinetic energy of a molecule in a gas is $E_1$. The kinetic energy of the electron (e) accelerated from rest through potential difference 'V' volt is $E_2$. The temperature at which $E_1 = E_2$ possible is (mass of molecule and electron is same) (N = number of molecules, V = Velocity, R = gas constant)