Question

Two liquids, A and B, have equal masses and equal initial temperatures. Each is heated for the same length of time over identical burners. Afterward, liquid A is hotter than liquid B. Which has the larger specific heat?a.Liquid B.b.Liquid A.c.There's not enough information to tell.

Answer 1

Liquid B

Step-by-step explanation:

The amount of heat energy that must be supplied to a substance in order to increase its temperature is given by:

`Q=mC\Delta T`

where

m is the mass of the substance

C is the specific heat capacity of the substance

`\Delta T` is the increase in temperature

The equation can be rewritten as

`C=(Q)/(m\Delta T)`

In this problem, we know that:

- Liquid A and B have same mass,
`m_A = m_B = m`

- The two liquids have same initial temperature, but afterwards liquid A is hotter than liquid B; this means that
`\Delta T_A > \Delta T_B`

- Moreover, the two liquids are heated for the same time over identical burners: this means that the amount of heat supplied is the same for the two liquids,
`Q_A=Q_B`

By looking at the equation, we see that since Q and m are the same for the two liquids, then their specific heat is just inversely proportional to the change in temperature: and since the change in temperature is larger for liquid A, this means that the specific heat is larger for liquid B.