Here we have to calculate the heat required to raise the temperature of water from 85.0 ⁰F to 50.4 ⁰F.
10.857 kJ heat will be needed to raise the temperature from 50.4 ⁰F to 85.0 ⁰F
The amount of heat required to raise the temperature can be obtained from the equation H = m×s×(t₂-t₁).
Where H = Heat, s =specific gravity = 4.184 J/g.⁰C, m = mass = 135.0 g, t₁ (initial temperature) = 50.4 ⁰F or 10.222 ⁰C and t₂ (final temperature) = 85.0⁰F or 29.444 ⁰C.
On plugging the values we get:
H = 135.0 g × 4.184 J/g.⁰C×(29.444 - 10.222) ⁰C
Or, H = 10857.354 J or 10.857 kJ.
Thus 10857.354 J or 10.857 kJ heat will be needed to raise the temperature.
(a) 3347 J; (b) 3043 J; (c) 58 J/K; (d) 35.5 °C
(a) Heat lost by copper
The formula for the heat lost or gained by a substance is
ΔT = T₂ - T₁= 30.3 °C - 100.4 °C = -70.1 °C = -70.1 K
q = 124.0 g × 0.385 J·K⁻¹g⁻¹ × (-70.1 K) = -3347 J
The negative sign shows that heat is lost.
The copper block has lost 3347 J.
(b) Heat gained by water
ΔT = 30.3 °C - 25.1 °C = 5.2 °C = 5.2 K
q = 140.0 g × 4.18 J·K⁻¹g⁻¹ × 5.2 K = 3043 J
The water has gained 3043 J.
(c) Heat capacity of calorimeter
Heat lost by Cu = heat gained by water + heat gained by calorimeter
The temperature change for the calorimeter is the same as that for the water.
ΔT = 5.2 K
The heat capacity of the calorimeter is 58 J/K.
(d) Final temperature of water
The final temperature of the water would be 35.5 °C.
The amount of energy required will be 1400.61 KJ.
Mass of water liquid m= 497 g
Mole ,n= m/18
Total heat=Latent heat of water at constant temperature 0°C + Sensible heat of water from temperature 0 °C to 100° C+Sensible heat of steam from 100 °C to 167°C.
We know that
Sensible heating =m Cp ΔT
So the total heat ,Q
Q= 27.6 x 40.79 x 1000 + 497 x 4.184 x 100+ 497 x 1.99 x 67 J
So the amount of energy required will be 1400.61 KJ.