An electric heater raises the temperature of 120g of water in a thin light vessel through 10K in 2mins, when placed in 70g of water contained in a metal vessel of mass 0.55kg the temperature rises through 9K in the same time. Calculate from the above:
a)the heat supplied in 2mins
b)the power of the heater
c)the heat supplied to the 70g of water
d)the heat supplied to the metal vessel
e)the heat capacity of the vessel
f) the specific heat capacity of its material (specific heat capacity of water = 4200)
To solve this problem, we need to use the formula:
Q = mcΔT
where Q is the heat supplied, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
Let's solve the questions one by one:
a) The heat supplied in 2 minutes:
We are given the mass of water as 120g and the change in temperature as 10K. Using the formula above, we can calculate the heat supplied:
Q = (120g)(4200)(10K)
Q = 5,040,000 J (Joules)
So, the heat supplied in 2 minutes is 5,040,000 Joules.
b) The power of the heater:
Power (P) is defined as the rate at which work is done or energy is transferred. It is the amount of energy transferred per unit time.
Power (P) = Energy (Q) / Time (t)
Given that the time is 2 minutes (which is 120 seconds) and the energy supplied is 5,040,000 Joules, we can calculate the power:
P = 5,040,000 J / 120 s
P ≈ 42,000 W (Watts)
So, the power of the heater is approximately 42,000 Watts.
c) The heat supplied to the 70g of water:
Using the same formula, we can calculate the heat supplied to the 70g of water:
Q = (70g)(4200)(9K)
Q = 2,646,000 J
So, the heat supplied to the 70g of water is 2,646,000 Joules.
d) The heat supplied to the metal vessel:
To calculate the heat supplied to the metal vessel, we need to consider the mass of the vessel and its heat capacity.
The mass of the metal vessel is given as 0.55kg. Let's assume the heat capacity of the metal vessel as C.
Q = mcΔT
Q = (0.55kg)(C)(9K)
We don't have the value of C, so we can't calculate the exact heat supplied to the metal vessel. We can only solve for C if we have additional information.
e) The heat capacity of the vessel:
We can calculate the heat capacity of the vessel by rearranging the formula:
Q = mcΔT
C = Q / (mΔT)
Substituting the given values, we get:
C = 2,646,000 J / (70g)(9K)
C ≈ 530 J/K
So, the heat capacity of the vessel is approximately 530 J/K.
f) The specific heat capacity of its material:
To find the specific heat capacity of the material, we need to know the mass of the vessel and the heat capacity of the vessel's material. Unfortunately, these values are not provided, so we cannot calculate the specific heat capacity.