The same amount of heat entering identical masses of different substances produces different temperature changes. Calculate the final temperature when 1.25 kcal of heat enters 1.25 kg of the following, originally at 20.0°C.

(a) water
(b) concrete
(c) steel
(d) mercury

To calculate the final temperature when a certain amount of heat enters a substance, we can use the equation:

q = m * c * ΔT

where
q is the heat absorbed or released,
m is the mass of the substance,
c is the specific heat capacity of the substance, and
ΔT is the change in temperature.

We can rearrange the equation to solve for ΔT:

ΔT = q / (m * c)

Let's calculate the final temperature for each substance.

(a) Water:
The specific heat capacity of water is approximately 4.18 J/g°C or 1 calorie/gram °C.
Converting kcal to calories: 1.25 kcal = 1250 calories.
Converting kg to grams: 1.25 kg = 1250 grams.

ΔT_water = 1250 calories / (1250 g * 4.18 J/g°C)
= 0.238°C

The final temperature of water will be 20.0°C + 0.238°C = 20.238°C.

(b) Concrete:
The specific heat capacity of concrete is approximately 0.84 J/g°C or 0.20 calorie/gram °C.

ΔT_concrete = 1250 calories / (1250 g * 0.84 J/g°C)
= 1.488°C

The final temperature of concrete will be 20.0°C + 1.488°C = 21.488°C.

(c) Steel:
The specific heat capacity of steel is approximately 0.49 J/g°C or 0.12 calorie/gram °C.

ΔT_steel = 1250 calories / (1250 g * 0.49 J/g°C)
= 4.082°C

The final temperature of steel will be 20.0°C + 4.082°C = 24.082°C.

(d) Mercury:
The specific heat capacity of mercury is approximately 0.14 J/g°C.

ΔT_mercury = 1250 calories / (1250 g * 0.14 J/g°C)
= 62.5°C

The final temperature of mercury will be 20.0°C + 62.5°C = 82.5°C.

Therefore, the final temperatures are:
(a) Water: 20.238°C
(b) Concrete: 21.488°C
(c) Steel: 24.082°C
(d) Mercury: 82.5°C

To calculate the final temperature when a certain amount of heat enters a substance, we can use the equation:

Q = mcΔT

Where:
Q is the heat input or the energy gained by the substance (in joules)
m is the mass of the substance (in kilograms)
c is the specific heat capacity of the substance (in joules per kilogram per degrees Celsius)
ΔT is the change in temperature (final temperature - initial temperature) of the substance (in degrees Celsius)

To answer the question:

(a) For water:
The specific heat capacity of water is approximately 4.18 J/g°C or 4,180 J/kg°C.

First, convert the given heat input from kcal to Joules:
1 kcal = 4.18 kJ = 4,180 J
So, 1.25 kcal = 1.25 * 4,180 J = 5,225 J

Using the equation Q = mcΔT, we can rearrange it to find ΔT:
ΔT = Q / (mc)

Substituting the values:
ΔT = 5,225 J / (1.25 kg * 4,180 J/kg°C)

Calculating, we find:
ΔT = 0.995°C

Since the initial temperature was 20.0°C, the final temperature will be:
Final temperature = Initial temperature + ΔT = 20.0°C + 0.995°C = 20.995°C

Therefore, the final temperature of water is approximately 20.995°C.

(b) For concrete:
The specific heat capacity of concrete can vary depending on the composition, but for general purposes, let's assume it is around 0.84 J/g°C or 840 J/kg°C.

Using the same process as for water:
ΔT = Q / (mc)

Substituting the values:
ΔT = 5,225 J / (1.25 kg * 840 J/kg°C)

Calculating, we find:
ΔT = 5.94°C

The final temperature of concrete will be:
Final temperature = Initial temperature + ΔT = 20.0°C + 5.94°C = 25.94°C

Therefore, the final temperature of concrete is approximately 25.94°C.

(c) For steel:
The specific heat capacity of steel is around 0.46 J/g°C or 460 J/kg°C.

Using the same process as before:
ΔT = Q / (mc)

Substituting the values:
ΔT = 5,225 J / (1.25 kg * 460 J/kg°C)

Calculating, we find:
ΔT = 9.52°C

The final temperature of steel will be:
Final temperature = Initial temperature + ΔT = 20.0°C + 9.52°C = 29.52°C

Therefore, the final temperature of steel is approximately 29.52°C.

(d) For mercury:
The specific heat capacity of mercury is around 0.14 J/g°C or 140 J/kg°C.

Using the same process as before:
ΔT = Q / (mc)

Substituting the values:
ΔT = 5,225 J / (1.25 kg * 140 J/kg°C)

Calculating, we find:
ΔT = 29.71°C

The final temperature of mercury will be:
Final temperature = Initial temperature + ΔT = 20.0°C + 29.71°C = 49.71°C

Therefore, the final temperature of mercury is approximately 49.71°C.

1.25 kcal = 5233.5 J

c(merc) = 139 J/kg•K
c(steel) = 470 J/kg•K
c(concrete) = 880 J/kg•K
c(water) = 4183 J/kg•K

ΔT=Q/mc =5233.5/1.25• 139 =30.1º => 50,1º
ΔT=Q/mc =5233.5/1.25•470 =8.91º =>
28,91º
ΔT=Q/mc =5233.5/1.25•880 =4.8º =>
24,8º
ΔT=Q/mc =5233.5/1.25•4183 =1º =>
21º