The temperature of a gas is $$-50^{\circ} \mathrm{C}$$. To what temperature the gas should be heated so that the rms speed is increased by $$3$$ times?

A Carnot engine has an efficiency of $$50 \%$$ when its source is at a temperature $$327^{\circ} \mathrm{C}$$. The temperature of the sink is :-

An ideal gas follows a process described by the equation $$P{V^2} = C$$ from the initial $$({P_1},\,{V_1},\,{T_1})$$ to final $$({P_2},\,{V_2},\,{T_2})$$ thermodynamic states, where C is a constant. Then

Two rods one made of copper and other made of steel of same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are 385 J s^{$$-$$1} K^{$$-$$1} m^{$$-$$1} and 50 J s^{$$-$$1} K^{$$-$$1} m^{$$-$$1} respectively. The free ends of copper and steel are held at 100$$^\circ$$C and 0$$^\circ$$C respectively. The temperature at the junction is, nearly :