Question

A solid cube of mass \( m \) at a temperature \( \theta_0 \) is heated at a constant rate. It becomes liquid at temperature \( \theta_1 \), and vapor at temperature \( \theta_2 \). Let \( s_1 \) and \( s_2 \) be specific heats in its solid and liquid states respectively. If \( L \) and \( L_v \) are latent heats of fusion and vaporization respectively, then the minimum heat energy supplied to the cube until it vaporises is

• A. \( m c_1 (\theta_1 - \theta_0) + m c_2 (\theta_2 - \theta_1) + m L_v \)
• B. \( m L_f + m c_2 (\theta_2 - \theta_1) + m L_v \)
• C. \( m (\theta_2 - \theta_0) + m L_v \)
• D. \( m c_1 (\theta_1 - \theta_0) + m L_f + m L_v \)

Answer 1

The Correct Option is A

The total heat energy required to vaporize the cube is the sum of:
1) The heat to raise the temperature of the solid from \( \theta_0 \) to \( \theta_1 \): \( m c_1 (\theta_1 - \theta_0) \), 
2) The heat to melt the solid into liquid: \( m L_f \), 
3) The heat to raise the temperature of the liquid from \( \theta_1 \) to \( \theta_2 \): \( m c_2 (\theta_2 - \theta_1) \), 
4) The heat to vaporize the liquid: \( m L_v \).