A copper block of mass 100g at a temperature of 150 degree celcius is dropped into a copper calorimeter of 40g containing 80g of water at 30 degree celcius. Calculate the steady final temperature of the mixture assuming no heat is lost to the surrounding.(s.h.c of copper and water are 400jkg-1k-1 and 4200jkg-1k-1)
difference in deg C is same as deg K
copper block loses = 0.100 kg * 400 (150 -T)deg C
copper pot gains 0.040 * 400 *(T- 30)
water gains 0.080 * 4200 (T-30)
so
0.1 * 400 * (150-T) = [ 0.04*400 + 0.08*4200] (T-30)
plug and chug
Pls urgent
To calculate the steady final temperature of the mixture, we can use the principle of conservation of energy. The heat lost by the hot copper block will be equal to the heat gained by the calorimeter and water.
First, let's calculate the heat lost by the copper block:
Q1 = mcΔT1
where
Q1 is the heat lost by the copper block,
m is the mass of the copper block,
c is the specific heat capacity of copper, and
ΔT1 is the change in temperature of the copper block.
Given:
m = 100 g
c = 400 J/kg·K
ΔT1 = (final temperature - initial temperature) = (final temperature - 150°C)
Next, we can calculate the heat gained by the calorimeter and water:
Q2 = mcΔT2
where
Q2 is the heat gained by the calorimeter and water,
m is the total mass of the calorimeter and water,
c is the specific heat capacity of water, and
ΔT2 is the change in temperature of the calorimeter and water.
Given:
m = 40 g + 80 g = 120 g
c = 4200 J/kg·K
ΔT2 = (final temperature - initial temperature) = (final temperature - 30°C)
According to the principle of conservation of energy, Q1 = Q2. Therefore, we have:
mcΔT1 = mcΔT2
Substituting the given values, we can solve for the final temperature.
100 g * 400 J/kg·K * (final temperature - 150°C) = 120 g * 4200 J/kg·K * (final temperature - 30°C)
40000 J/K * (final temperature - 150°C) = 504000 J/K * (final temperature - 30°C)
40000 * final temperature - 6000000 = 504000 * final temperature - 15120000
40000 * final temperature - 504000 * final temperature = -15120000 + 6000000
-464000 * final temperature = -9120000
final temperature = -9120000 / -464000 ≈ 19.66°C
Therefore, the steady final temperature of the mixture is approximately 19.66°C.
To calculate the final temperature of the mixture, we can use the principle of conservation of energy.
The heat lost by the copper block (mcΔTc) will be equal to the heat gained by the water in the calorimeter (mwΔTw) and the calorimeter itself (msΔTs). The equations for the heat lost and gained can be written as:
Heat lost by copper block = Heat gained by water + Heat gained by calorimeter
Using the formula for heat transfer (Q=mcΔT), we can write:
(mass of copper block) * (specific heat capacity of copper) * (change in temperature of copper)
= (mass of water) * (specific heat capacity of water) * (change in temperature of water)
+ (mass of calorimeter) * (specific heat capacity of calorimeter) * (change in temperature of calorimeter)
Now let's plug in the given values:
Mass of copper block (mc) = 100g
Specific heat capacity of copper = 400 J/kg·K
Initial temperature of copper block = 150°C (which needs to be converted to Kelvin)
Mass of water (mw) = 80g
Specific heat capacity of water = 4200 J/kg·K
Initial temperature of water = 30°C (which also needs to be converted to Kelvin)
Mass of calorimeter (ms) = 40g
Specific heat capacity of calorimeter = ??? (The specific heat capacity of the calorimeter was not given, so we need to assume a value for it or look it up.)
Change in temperature of copper (ΔTc) = Final temperature of mixture - Initial temperature of copper
Change in temperature of water (ΔTw) = Final temperature of mixture - Initial temperature of water
Change in temperature of calorimeter (ΔTs) = Final temperature of mixture - Initial temperature of calorimeter (which can be assumed to be the same as the initial temperature of water, since they are both at 30°C)
Now we can rearrange the equation and solve for the final temperature of the mixture.