The density of water at 4°C is 1.00 x 10³ kg / m³. What is wat...

Question

The density of water at 4°C is 1.00 x 10³ kg / m³. What is water’s density at 94°C? Assume a constant coefficient of volume expansion.

Accepted Answer

Welcome back everyone. In this problem. A certain type of oil has a density of two multiplied by 10 to the third kilograms per cubic meter at five °C. Calculate the density of this oil at 96 °C. Assume the volume expansion coefficient is 240 multiplied by 10 to the negative sixth per degree Celsius. A says it's 1957 kg per cubic meter. B 2940 kg per cubic meter. C 3155 kg per cubic meter and d 4591 kg per cubic meter. Now we're trying to figure out the density of our oil at a new temperature or at a different temperature. OK. So let's make a note of all the information that we have here. What do we know? Well, so far we know that our oil has a density of two multiplied by 10 to the third kilograms per cubic meter at five °C. In other words, that tells us the initial density of the oil. OK? Is that density value and the initial temperature of the oil, let's call that T knot OK, is equal to five °C. And we leave our temperature in Celsius because our volume expansion coefficient is also in Celsius. Next, the problem tells us that our final temperature is 96 °C. So let's call that temperature T OK. And for that temperature, we want to find what the density is going to be equal to. So here we have two scenarios. First of all, let's ask ourselves, what do we know about density? Well, for starters recall that density is defined as the mass per unit of volume. OK. So if we want to find our density here, this is the formula that we could use. But from our information, we are also given the initial density and the initial density will be equal to the mass divided by the initial volume. The mass stays the same in that case. Then since the mass stays the same, that means the mass is going to be equal to the density, the initial density multiplied by the initial volume. And now, if we substitute that into our formula for density, that means our density is going to be equal to the initial density multiplied by the initial volume divided by the volume at 96 °C. So now we'll need to figure out what that volume is. So how can we find the value of V? Well, what do we know? Well, we also know that that volume V is going to be equal to the initial volume plus the change in volume because of the change in temperature. OK. And that change in volume is going to be equal to the coefficient of volumetric expansion. In this case, or coefficient for our oil multiplied by our initial volume. V not OK, multiplied by our change in temperature. And we can figure out what those values are because now if we were to substitute, we know that beta equals 240 multiplied by 10 to the negative six per degree Celsius. OK? We have our initial volume. We leave that as V not, we don't know it yet, but we'll keep it for. No. And our change in temperature is going to be 96 °C minus five °C. And now if we go ahead and simplify here, we can express our change in volume in terms of VNO, OK? Which is going to be equal to 0.02184 V knot. No, I'm gonna put this in a box here because since we have our change or let me just, we try to draw a better box because no, now that we have our change in volume, we can substitute it into our formula for V because now that tells us that V then, but weird is gonna be equal to V knot plus that change, which is in terms of V knot, 0.02. Let me write that properly here. 0.02184 V knot, which tells us that our final volume is equal to 1.02184 multiplied by our initial volume. Now that we have our final volume in terms of our initial volume. And our formula for a density has the initial volume included, we can substitute and simplify because no, this tells us then that our density OK, we put that back in black because the, the initial uh color it was in is going to be equal to our initial density multiplied by V knot divided by V which is 1.02184 V knot V not cancers. So that means our density is going to be equal to our initial density divided by 1.02184 which when we substitute our known values, that's going to be equal to two multiplied by 10 to the third kilograms per cubic meter divided by 1.02184. Which when we simplify, we get it to be approximately equal to 1957 kg per cubic meter to the nearest kilogram per cubic meter. Therefore, this is going to be our density when our oil is heated to 96 °C. If we look back at our answer choices, that means a is the correct answer. Thanks for watching everyone. I hope this video helped.

The density of water at 4°C is 1.00 x 10³ kg / m³. What is water’s density at 94°C? Assume a constant coefficient of volume expansion.

Key Concepts

Density

Coefficient of Volume Expansion

Thermal Expansion

Watch next