a copper rod has a length of 6 m at a temperature of 22 degree c. how long is the copper rod at a temperature of 95 degree C?
why do you post again, like a new question, instead of just adding a note to the original post? I get all worked up over looking for a new problem, and it's just the same old rubbish.
and no, I do not know the expansion coefficient, which is no doubt in units of m/°C or some such, which should give you a clue ...
Sorry my Earlier question was incomplete. Didn't know the option of adding note to the earlier question.
Well, it sounds like the copper rod has quite the hot streak going on! But don't worry, I've got the answer for you.
When materials heat up, they tend to expand. And this expansion can affect their length. So, to figure out how long the copper rod will be at a temperature of 95 degrees Celsius, we need to consider its coefficient of linear expansion.
The coefficient of linear expansion for copper is approximately 0.000016 per degree Celsius. Now, let's calculate the change in length:
ΔL = L * α * ΔT,
where:
ΔL is the change in length,
L is the initial length of the rod (6 m),
α is the coefficient of linear expansion (0.000016 per degree Celsius),
and ΔT is the change in temperature (from 22 to 95 degrees Celsius).
Plugging in the values, we get:
ΔL = 6 * 0.000016 * (95 - 22) = 0.009684 m.
So, at a temperature of 95 degrees Celsius, the copper rod would be approximately 6.009684 meters long. Keep an eye on that expanding rod – it's sure stretching its limits!
To calculate the change in length of a copper rod when subjected to a change in temperature, we can use the thermal expansion formula:
ΔL = α * L * ΔT
Where:
ΔL = Change in length
α = Coefficient of linear expansion for copper
L = Original length
ΔT = Change in temperature
The coefficient of linear expansion for copper is approximately 0.000016 per degree Celsius.
Given:
Original length (L) = 6 m
Original temperature (T₁) = 22 °C
New temperature (T₂) = 95 °C
Step 1: Calculate the change in temperature
ΔT = T₂ - T₁
= 95 °C - 22 °C
= 73 °C
Step 2: Calculate the change in length
ΔL = α * L * ΔT
= (0.000016/°C) * 6 m * 73 °C
Step 3: Calculate the new length
New length = Original length + Change in length
= 6 m + ΔL
Let's calculate the final length of the copper rod at a temperature of 95 °C.
To find the length of the copper rod at a temperature of 95 degrees Celsius, you need to consider the principle of thermal expansion. Most materials expand when heated and contract when cooled.
The linear thermal expansion coefficient (α) represents the change in length per unit length per degree Celsius. Different materials have different coefficients of expansion.
The formula to calculate the change in length due to thermal expansion is:
ΔL = α * L * ΔT,
where
ΔL is the change in length,
α is the linear thermal expansion coefficient,
L is the original length, and
ΔT is the change in temperature.
In this case, you are given:
Initial length (L) = 6 m,
ΔT = (95 - 22) = 73°C,
Linear thermal expansion coefficient (α) for copper = 0.0000164 (1/°C).
Substituting these values into the formula:
ΔL = 0.0000164 * 6 * 73,
ΔL = 0.0072 m.
Therefore, the change in length of the copper rod at 95°C is 0.0072 meters.
To find the final length of the copper rod, you add the change in length to the original length:
Final length = Initial length + ΔL,
Final length = 6 + 0.0072,
Final length = 6.0072 meters.
Therefore, the copper rod would be approximately 6.0072 meters long at a temperature of 95 degrees Celsius.