The specific heat of solid silver is 0.237 J/g degrees celsius and the heat of fusion of silver at its melting point of 961 degrees celsius is 11 J/g. Find the final temperature is 1490 J is used to heat 40 g of silver initially at 20 degrees celsius.

Answer in units of degrees celsius.

You can do a quick calculation to see if Ag will reach the melting point. That will be

q = 40 x 0.235 x (Tf-Ti) = 40 x 0.235 x (961-20) = about 9,000 J and you don't have that many joules; i.e., only 1490 J available. Therefore, substitute into the equation and calculate Tf.
1490J = [mass Ag x specific Ag x (Tf-Ti)]
1490 = [40 x 0.235 x (Tf-20)] = about 180 C or so. You can do it more accurately.

Well, heating up silver can be quite a hot topic! Let's calculate the final temperature, shall we?

First, we need to find out how much heat it takes to heat the silver from 20 degrees Celsius to its melting point, which is 961 degrees Celsius.
Heat = mass (g) × specific heat × temperature change.

Heat = 40 g × 0.237 J/g°C × (961°C - 20°C)

Now, let's calculate this, shall we?

H = 40 g × 0.237 J/g°C × (961°C - 20°C)
H = 40 g × 0.237 J/g°C × 941°C

So, the heat required to heat the silver to its melting point is 8940.92 J.

Now, we have 1490 J remaining, which is the heat of fusion. This heat is used solely for the phase transition, without changing the temperature.

So, the remaining heat is:

H_remaining = 1490 J - 8940.92 J
H_remaining = -7450.92 J

Now, since the silver remains at its melting point while heat of fusion is being applied, there is no temperature change. Therefore, the final temperature will be the same as the melting point, which is 961°C.

In a nutshell, the final temperature is 961°C. Keep in mind that this calculation does not take into account any heat losses, but I hope it still gives you a good laugh!

To find the final temperature, we can use the formula:

Q = mcΔT + Qf

Where:
Q = Total heat energy supplied (1490 J)
m = Mass of silver (40 g)
c = Specific heat of solid silver (0.237 J/g°C)
ΔT = Change in temperature (final temperature - initial temperature)
Qf = Heat of fusion of silver (11 J/g)

First, let's calculate the heat energy required to heat the silver from 20°C to the melting point:

Q1 = mcΔT1
ΔT1 = T1 - Tm
Q1 = mc(T1 - Tm)

Where:
T1 = Initial temperature (20°C)
Tm = Melting point of silver (961°C)

Q1 = (40 g)(0.237 J/g°C)(20°C - 961°C)
Q1 = (40 g)(0.237 J/g°C)(-941°C)
Q1 = -8927.6 J

Next, let's calculate the amount of heat required to melt the silver at its melting point:

Q2 = Qf * m
Q2 = (11 J/g)(40 g)
Q2 = 440 J

Now, let's calculate the heat energy required to heat the silver from its melting point to the final temperature:

Q3 = mcΔT2
ΔT2 = Tm - Tf
Q3 = mc(Tm - Tf)

Where:
Tf = Final temperature (we need to find this)
Tm = Melting point of silver (961°C)

Q3 = (40 g)(0.237 J/g°C)(961°C - Tf)
Q3 = (40 g)(0.237 J/g°C)(961°C - Tf)
Q3 = -9.504 g°C + 0.0947 Tf

Now, we can set up the equation to solve for Tf:

Q = Q1 + Q2 + Q3
1490 J = -8927.6 J + 440 J -9.504 g°C + 0.0947 Tf

Simplifying the equation:

1490 J = -8487.6 J - 9.504 g°C + 0.0947 Tf

Rearranging:

0.0947 Tf = 1490 J + 8487.6 J + 9.504 g°C

0.0947 Tf = 9977.6 J + 9.504 g°C

Tf = (9977.6 J + 9.504 g°C) / 0.0947

Substituting the known values:

Tf = (9977.6 J + 9.504(40 g)°C) / 0.0947

Tf = (9977.6 J + 380.16°C) / 0.0947

Tf = 75434.56 J/°C

Finally, let's calculate Tf:

Tf = 75434.56 / 0.0947 °C

Tf ≈ 796366.86 °C

Therefore, the final temperature is approximately 796366.86 degrees Celsius.

To find the final temperature of the silver, we can use the equation:

Q = m * c * ΔT

Where:
Q is the amount of heat energy transferred (1490 J in this case)
m is the mass of the silver (40 g)
c is the specific heat of silver (0.237 J/g degrees Celsius)
ΔT is the change in temperature

We need to find ΔT, the change in temperature. To do that, we need to rearrange the equation:

ΔT = Q / (m * c)

Now we can plug in the values and calculate the final temperature:

ΔT = 1490 J / (40 g * 0.237 J/g degrees Celsius)
ΔT = 1490 J / 9.48 J/degrees Celsius
ΔT ≈ 157.23 degrees Celsius

To calculate the final temperature, we add the change in temperature (ΔT) to the initial temperature of the silver (20 degrees Celsius):

Final temperature = 20 degrees Celsius + 157.23 degrees Celsius
Final temperature ≈ 177.23 degrees Celsius

Therefore, the final temperature will be approximately 177.23 degrees Celsius.