HELP im stuck on my homework
1. A 15.75-g piece of iron absorbs 1086.75 joules of heat energy, and its temperature changes from 25°C to 175°C. Calculate the specific heat capacity of iron.
2. How many joules of heat are needed to raise the temperature of 10.0 g of aluminum from 22°C to55°C, if the specific heat of aluminum is 0.90 J/g°C?
3. To what temperature will a 50.0 g piece of glass raise if it absorbs 5275 joules of heat and its specific heat capacity is 0.50 J/g°C? The initial temperature of the glass is 20.0°C.
4. Calculate the heat capacity of a piece of wood if 1500.0 g of the wood absorbs 6.75×104joules of heat, and its temperature changes from 32°C to 57°C.
5. 100.0 mL of 4.0°C water is heated until its temperature is 37°C. If the specific heat of water is 4.18 J/g°C, calculate the amount of heat energy needed to cause
1. To calculate the specific heat capacity of iron, we can use the formula:
Q = m * c * ΔT
where Q is the heat energy absorbed (in joules), m is the mass of the iron (in grams), c is the specific heat capacity of iron, and ΔT is the change in temperature (in °C).
In this case, we have:
Q = 1086.75 J
m = 15.75 g
ΔT = 175°C - 25°C = 150°C
Plugging in these values, we get:
1086.75 J = 15.75 g * c * 150°C
To solve for c, we divide both sides of the equation by (15.75 g * 150°C):
c = 1086.75 J / (15.75 g * 150°C)
c ≈ 0.485 J/g°C
Therefore, the specific heat capacity of iron is approximately 0.485 J/g°C.
2. To calculate the heat energy required to raise the temperature of aluminum, we again use the formula:
Q = m * c * ΔT
where Q is the heat energy required (in joules), m is the mass of aluminum (in grams), c is the specific heat capacity of aluminum, and ΔT is the change in temperature (in °C).
In this case, we have:
m = 10.0 g
c = 0.90 J/g°C
ΔT = 55°C - 22°C = 33°C
Plugging in these values, we get:
Q = 10.0 g * 0.90 J/g°C * 33°C
Q ≈ 297 J
Therefore, approximately 297 joules of heat energy are needed to raise the temperature of 10.0 g of aluminum from 22°C to 55°C.
3. To calculate the final temperature of the glass, we can rearrange the formula:
Q = m * c * ΔT
to solve for ΔT:
ΔT = Q / (m * c)
In this case, we have:
Q = 5275 J
m = 50.0 g
c = 0.50 J/g°C
The initial temperature, T_initial = 20.0°C.
Plugging in these values, we get:
ΔT = 5275 J / (50.0 g * 0.50 J/g°C)
ΔT = 5275 J / 25.0 J/°C
ΔT = 211°C
To find the final temperature, T_final, we add ΔT to the initial temperature:
T_final = T_initial + ΔT
T_final = 20.0°C + 211°C
T_final ≈ 231°C
Therefore, the glass will raise to approximately 231°C if it absorbs 5275 joules of heat energy.
4. The heat capacity of a substance is the amount of heat energy required to raise its temperature by 1°C. We can calculate the heat capacity using the formula:
C = Q / ΔT
where C is the heat capacity (in joules per °C), Q is the heat energy absorbed (in joules), and ΔT is the change in temperature (in °C).
In this case, we have:
Q = 6.75 × 10^4 J
m = 1500.0 g
ΔT = 57°C - 32°C = 25°C
Plugging in these values, we get:
C = 6.75 × 10^4 J / 25°C
C = 2.7 × 10^3 J/°C
Therefore, the heat capacity of the piece of wood is 2.7 × 10^3 joules per °C.
5. To calculate the amount of heat energy needed to raise the temperature of water, we use the formula:
Q = m * c * ΔT
where Q is the heat energy required (in joules), m is the mass of water (in grams), c is the specific heat capacity of water, and ΔT is the change in temperature (in °C).
In this case, we have:
m = 100.0 mL = 100.0 g (since 1 mL of water has a mass of 1 g)
c = 4.18 J/g°C
ΔT = 37°C - 4°C = 33°C
Plugging in these values, we get:
Q = 100.0 g * 4.18 J/g°C * 33°C
Q ≈ 13794 J
Therefore, approximately 13794 joules of heat energy are needed to raise the temperature of 100.0 g of water from 4°C to 37°C.