Question

The relationship between heat transfer and change in temperature is given by Q = mct, where c is specific heat capacity. Under what conditions will c = Q?


a. m = 1 kg T = 1 oC
b. m = 1 g T = 10 oC
c. m = 10 g T = 10 oC
d. m = 100 g T = 10 oC
e. m = 1 g T = 1 oC

Answer 1

From Q = m c t, if c = Q then Q = m Q t. Either Q = 0 (trivial) or 1 = m t, so the nontrivial condition is

m · ΔT = 1 (with m in kg, ΔT in °C).

Check each option (convert grams → kg):
- a: 1 kg · 1°C = 1 → yes
- b: 0.001 kg · 10°C = 0.01 → no
- c: 0.01 kg · 10°C = 0.1 → no
- d: 0.1 kg · 10°C = 1 → yes
- e: 0.001 kg · 1°C = 0.001 → no

So options a and d.