Question

The specific heat for substance $A$ is twice the specific heat of substance $B$. The same mass of each substance is allowed to gain $50$ Joules of heat energy. As a result of the heating process:

• A. the temperature of $A$ rises twice as much as $B$
• B. the temperature of $A$ rises four times as much as $B$
• C. the temperature of $B$ rises twice as much as $A$
• D. the temperature of $B$ rises four times as much as $A$
• E. the temperature of both $B$ and $A$ rise the same amount

Answer 1

The correct option is C the temperature of $B$ rises twice as much as $A$

Let specific heat of substance $A$ is $2c$ and specific heat of substance $B$ is $c$ ,

we have , heat given $Q=mc\Delta t$, where $\Delta t$ denotes change in temperature ,

so , for substance $A$, $Q=m\times 2c\Delta t_A$

or $\Delta t_A=Q/2mc$ .........eq1

For substance $B$ , $Q=mc\Delta t_B$

$\Delta t_B=Q/mc$ ...................eq2

by eq1 and eq2,

$2\Delta t_A=\Delta t_B$