Question

A 5.0-gram sample of gold and a 5.0-gram sample of iron both absorb exactly 25 calories of energy. The specific heat of gold is 0.03 cal/g°C. The specific heat of iron is 0.11 cal/g°C. Which of the following statements is true?

The gold sample will experience a greater increase in temperature.
The iron sample will experience a greater increase in temperature.
Both samples will experience the same increase in temperature.

Answer 1

The gold sample will experience a greater increase in temperature.

Step-by-step explanation:

Answer 2

The gold sample will experience a greater increase in temperature.

Step-by-step explanation:

• To solve this problem, we can use the relation:

Q = m.c.ΔT,

where, Q is the amount of heat absorbed by substance.

m is the mass of the substance.

c is the specific heat of the substance.

ΔT is the difference between the initial and final temperature.

∴ ΔT = Q /(m.c)

It is clear that ΔT is inversely proportional to the specific heat capacity of the object.

So, the object with the smallest specific heat capacity (gold) will have the greater increase in temperature.

• The increase in T can be calculated for both objects:

For gold:

ΔT = Q /(m.c) = (25 cal)/(5.0 g)(0.03 cal/g°C) = 166.7°C.

For iron:

ΔT = Q /(m.c) = (25 cal)/(5.0 g)(0.11 cal/g°C) = 45.45°C.

• So, the right choice is:

The gold sample will experience a greater increase in temperature.