Question

Which of the following (with specific heat capacity provided) would show the smallest temperature change upon gaining 200.0 J of heat? A) 50.0 g Al, CAl = 0.903 J/g°C B) 50.0 g Cu, CCu = 0.385 J/g°C C) 25.0 g granite, Cgranite = 0.79 J/g°C D) 25.0 g Au, CAu = 0.128 J/g°C E) 25.0 g Ag, CAg = 0.235 J/g°C

Answer 1

Answer:

A) 50.0 g Al

Explanation:

We can calculate the temperature change of each substance by using the equation:

$\Delta T=\frac{Q}{mC_s}$

where

Q = 200.0 J is the heat provided to the substance

m is the mass of the substance

$C_s$ is the specific heat of the substance

Let's apply the formula for each substance:

A) m = 50.0 g, Cs = 0.903 J/g°C

$\Delta T=\frac{200}{(50)(0.903)}=4.4^{\circ}C$

B) m = 50.0 g, Cs = 0.385 J/g°C

$\Delta T=\frac{200}{(50)(0.385)}=10.4^{\circ}C$

C) m = 25.0 g, Cs = 0.79 J/g°C

$\Delta T=\frac{200}{(25)(0.79)}=10.1^{\circ}C$

D) m = 25.0 g, Cs = 0.128 J/g°C

$\Delta T=\frac{200}{(25)(0.128)}=62.5^{\circ}C$

E) m = 25.0 g, Cs = 0.235 J/g°C

$\Delta T=\frac{200}{(25)(0.235)}=34.0^{\circ}C$

As we can see, substance A) (Aluminium) is the one that undergoes the smallest temperature change.