A) 1 cal
B) 80 cal
C) 540 cal
Explanation:
A)
The amount of heat energy needed to raise the temperature of a certain mass of a substance is given by
[tex]Q=mC\Delta T[/tex]
where
m is the mass of the substance
C is the specific heat capacity
[tex]\Delta T[/tex] is the change in temperature
In this problem:
m = 1 g is the mass of water
[tex]C=1 cal/g^{\circ}C[/tex] is the specific heat capacity of water
[tex]\Delta T=1^{\circ}C[/tex] is the change in temperature
So, the heat needed is
[tex]Q=(1)(1)(1)=1 cal[/tex]
B)
For a solid substance at its melting point, the amount of heat needed to melt completely the substance is given by
[tex]Q=m\lambda_f[/tex]
where
m is the mass of the substance
[tex]\lambda_f[/tex] is the specific latent heat of fusion of the substance
In this problem:
- The ice is already at melting point, 0 °C
- Mass of the ice: [tex]m=1g[/tex]
- Specific latent heat of fusion of ice: [tex]\lambda_f=80 cal/g[/tex]
So, the heat needed is
[tex]Q=(1)(80)=80 cal[/tex]
C)
For a liquid substance at its boiling point, the amount of heat needed to boil completely the substance is given by
[tex]Q=m\lambda_v[/tex]
where
m is the mass of the substance
[tex]\lambda_v[/tex] is the specific latent heat of vaporization of the substance
In this problem:
- The water is already at boiling point, 100 °C
- Mass of the water: [tex]m=1g[/tex]
- Specific latent heat of vaporization of water: [tex]\lambda_v=540 cal/g[/tex]
So, the heat needed is
[tex]Q=(1)(540)=540 cal[/tex]
