Question

Two substances A and B have specific heats c and 2 c respectively. If A and B are given Q and 4Q amounts of heat respectively, the change in their temperatures is the same. If the mass of A is m, what is the mass of B?

Answer 1

Data: c (A) = c, c (B) = 2c, 

Q (A) = Q, Q (B) = 4Q, ΔT same, 

m (A) = m, m (B) = ?

Q = Mc ΔT ∴ ΔT = \(\cfrac{Q}{mc}\)

As ΔT is the same for substance A and B,

We have, \(\cfrac{Q(A)}{m(A)c(A)}\) = \(\cfrac{Q(B)}{m(B)c(B)}\)

∴ \(\cfrac{Q}{mc}\) = \(\cfrac{4Q}{m(B)2c}\)

∴ \(\cfrac{1}{m}\) = \(\cfrac{2}{m(B)}\)

∴ m(B) = 2m. 

This is the mass of B.