a copper container of mass 80g contains 60g of a liquid at 20 degree Celsius. a piece of copper of mass 100g and temperature 100 degree Celsius is dropped into the liquid. if the final temp of the system is 59.7 degree Celsius then the specific heat capacity of the liquid is:
a) 1
b) 0,092
c)0.066
d) 0.033
To find the specific heat capacity of the liquid, we can use the principle of heat transfer. The heat lost by the copper piece will be equal to the heat gained by the liquid and copper container.
First, let's calculate the heat lost by the copper piece:
Q1 = mcΔT1
where:
Q1 = heat lost by the copper piece
m = mass of the copper piece (100g)
c = specific heat capacity of copper (which is approximately 0.39 J/g·°C)
ΔT1 = change in temperature of the copper piece (100°C - 59.7°C)
Q1 = (100g)(0.39 J/g·°C)(100°C - 59.7°C)
Q1 = 1630.5 J
Next, let's calculate the heat gained by the liquid and the copper container:
Q2 = mcΔT2
where:
Q2 = heat gained by the liquid and copper container
m = mass of the liquid and copper container (80g + 60g = 140g)
c = specific heat capacity of the liquid (what we're trying to find)
ΔT2 = change in temperature of the liquid and copper container (59.7°C - 20°C)
Q2 = (140g)(c)(59.7°C - 20°C)
Q2 = 38.73c J
Since the heat lost is equal to the heat gained, we can set up an equation:
Q1 = Q2
1630.5 J = 38.73c J
Now, let's solve for c:
c = 1630.5 J / 38.73 J
c ≈ 42.07
From the provided answer choices, the specific heat capacity closest to 42.07 is:
b) 0.092
Therefore, the specific heat capacity of the liquid is approximately 0.092.