Question

The specific heat capacity of aluminum is about twice that of iron. Consider two blocks of equal mass, one made of aluminum and the other one made of iron, initially in thermal equilibrium.
Heat is added to each block at the same constant rate until it reaches a temperature of 500 K. Which of the following statements is true?
a. The iron takes less time than the aluminum to reach the final temperature.
b. The aluminum takes less time than the iron to reach the final temperature.
c. The two blocks take the same amount of time to reach the final temperature.

Answer 1

Answer:a

Explanation:

Given

Specific heat capacity of aluminium is twice that of iron.

$c_{Al}=2c_{iron}$

Also mass of two blocks is equal

Rate of heat added is also same

$\dot{Q_{Al}}=\dot{Q_{iron}}$

$\frac{Q_{Al}}{t_{Al}}=\frac{Q_{iron}}{t_{iron}}$

$\frac{mc_{Al}\Delta T}{t_{Al}}=\frac{mc_{iron}\Delta T}{t_{iron}}$

$\frac{2c_{iron}}{t_{Al}}=\frac{c_{iron}}{t_{iron}}$

$t_{Al}=2t_{iron}$

Thus Time taken by aluminium  block will be more