The amount of heat energy Q, used to heat up a substance depends on its mass m, its specific heat capacity (s) and the change in temperature Δ T of the substance. Using dimensional method, find the expression for s is (Given that .[s]=[L2 T-2 K-1]) is

Question

The amount of heat energy Q, used to heat up a substance depends on its mass m, its specific heat capacity (s) and the change in temperature Δ T of the substance. Using dimensional method, find the expression for s is (Given that .[s]=[L2 T-2 K-1]) is (A) Q m Δ T (B) (Q/m Δ T) (C) (Q m/Δ T) (D) (m/Q Δ T)

Tardigrade Admin · Accepted Answer

Q=ma sb θc [ ML 2 T -2]=[ M 9][ L 2 b T -2 b K -b][ K c ] ⇒ a=1, 2 b=2 ⇒ b=1 -b +c=0 ⇒ b=c ⇒ c=1 Q=m s Δ T ⇒ s=(Q/m Δ T)

Q. The amount of heat energy $Q$ , used to heat up a substance depends on its mass $m$ , its specific heat capacity $(s)$ and the change in temperature $Δ T$ of the substance. Using dimensional method, find the expression for $s$ is (Given that $[s] = [L^{2} T^{- 2} K^{- 1}])$ is

$Q m Δ T$

$\frac{Q}{m Δ T}$

$\frac{Q m}{Δ T}$

$\frac{m}{Q Δ T}$

$Q = m^{a} s^{b} θ^{c}$
$[M L^{2} T^{- 2}] = [M^{9}] [L^{2 b} T^{- 2 b} K^{- b}] [K^{c}]$
$\Rightarrow a = 1, 2 b = 2 \Rightarrow b = 1$
$- b + c = 0$
$\Rightarrow b = c \Rightarrow c = 1$
$Q = m s Δ T$
$\Rightarrow s = \frac{Q}{m Δ T}$

Q. The amount of heat energy Q, used to heat up a substance depends on its mass m, its specific heat capacity (s) and the change in temperature ΔT of the substance. Using dimensional method, find the expression for s is (Given that [s]=[L2T−2K−1]) is

QmΔT

mΔTQ​

ΔTQm​

QΔTm​