Calculating Heat Required to Warm Earth's Oceans by 1.0 °C

[jwainwright09]

Homework Statement
1.Global warming refers to the rise in average global temperature due to the increased concentration of certain gases, called greenhouse gases, in our atmosphere. Earth’s oceans, because of their high heat capacity, can absorb heat and therefore act to slow down global warming. How much heat would be required to warm Earth’s oceans by 1.0 °C? Assume that the volume of Earth’s oceans is 137 * 107 km3 and that the density of seawater is 1.03 g/cm3. Also assume that the heat capacity of seawater is the same as that of water.

Homework Equations

How much heat would be required to warm Earth’s oceans by 1.0 °C? Assume that the volume of Earth’s oceans is 137 * 107 km3 and that the density of seawater is 1.03 g/cm3. Also assume that the heat capacity of seawater is the same as that of water.

The Attempt at a Solution

Well I am not sure which formula to use. I am new to Chemistry and DO NOT understand it AT ALL. Do I use the d=m/v? I am so lost. If someone could work this same problem just with different numbers that would help me so much. If so, can you please show your work so that I can understand how to set up my problem and where to put the actual numbers in the equation or formula? Thanks so much!

 

[LawrenceC]

What is the formula for how much energy it takes to raise a n kg of water 1 degree C?

What is the mass of the oceans in kg?

Do the above questions suggest a way to solve this problem?

 

[jwainwright09]

Okay
1. It takes 1 calorie or c = 4.184 Joules or J to increase 1 gram of water by 1 degree celcius.

2. I am not sure how to answer what the mass of the oceans is in kg. This is what I am guessing. Take 137 x 107 km3 = 14659 km3? I am not sure this is right. And I am not sure what to do with the density of the sea water. What does it mean when it says to assume that the heat capacity of seawater is the same as that of water? Does this mean anything when working the problem?

 

[jwainwright09]

When working with the density of part, will I be using the solution: d=m/v? If so, I am assuming once I find out what the g is then I will divide that by 1.03 g/cm3. I am sorry to be such a pest, but I just want to understand this. I do not understand chemistry or math, so this is a challenge for me and my instructor is not helping work examples similar to our homework, so it leaves me more at a loss.

 

[LawrenceC]

http://hypertextbook.com/facts/2001/SyedQadri.shtml

The above link provides the volume of the oceans in cubic km. You know the density so use your formula d=m/v to get the mass. If d=m/v, then m=d(v)

Energy required is mass times specific heat times temperature change. Your units must agree with one another and they are handled algebraically. Don't multiply calories per gram by kilograms without first converting calories per gram to calories per kilogram. Likewise you have density in g/cm3. But the volume of the oceans is in km cubed. So you much convert to have uniform units.

 

[jwainwright09]

Okay.

D= 1.37 billion km^3
V= 1.03 g/cm^3
I have to find the mass.

Find m...

Do I have to convert km^3 to cm^3, then mulltiply density and volume to get the mass?

I do not know how to convert km^3 to cm^3.

Can you please help instruct me further?

 

[LawrenceC]

Okay.

D= 1.37 billion km^3
V= 1.03 g/cm^3
I have to find the mass.

Find m...

Do I have to convert km^3 to cm^3, then mulltiply density and volume to get the mass?

I do not know how to convert km^3 to cm^3.

Can you please help instruct me further?

In the equation d=m/v, d is the density, m is the mass, and v is the volume. Look at the units. You have your symbols, D and V, switched.

"Do I have to convert km^3 to cm^3, then mulltiply density and volume to get the mass?"

Yes, that is correct if you want to work in cm^3 units. You probably do because you have the density in grams/cm^3.

 

[jwainwright09]

Alright, I will switch the number for density and volume, but how do I convert km3 to cm3? I am still not understanding.

 

[jwainwright09]

Another question. Is this converstion for 1.37 billion km3 correct when converting to cm3? This is the answer I come up with:
1.4111 x 10^24 g/cm3? Do I leave off the last two digits of 11 behind the 41 to actually read 1.41 x 10^24 g/cm3?

Okay, now, if this IS correct, where does this play in with the specific heat capacity, specifically How much heat would be required to warm Earth’s oceans by 1.0 °C?

I come up with the difference in temerature is 1 degree Celcius assuming that the water was 1 degree C to begin with. Am I getting closer?

 

[berkeman]

Alright, I will switch the number for density and volume, but how do I convert km3 to cm3? I am still not understanding.

See my comments about unit conversions in this thread:

https://www.physicsforums.com/showthread.php?t=563087&highlight=multiply

.

 

[LawrenceC]

"1.4111 x 10^24 g/cm3? Do I leave off the last two digits of 11 behind the 41 to actually read 1.41 x 10^24 g/cm3?"

You have the density in 3 significant figures. Therefore you cannot have more than 3 significant figures in your final answer. You can carry all the extra figures through the calculation but only report the final answer in significant figures less than or equal to the least number of significant figures used in the multiplication.

In your statement above you are confusing density with mass. The 1.411 figure came from multiplying 1.03 g/cm^3 by the volume in cm^3. The units are handled just algebraic symbols. g/cm^3 times cm^3 = g.

 

[cindareally]

ok after reading all this I have figured out that the formula that I am using is d=m/v therefore: d= 1.03g/cm3 and m=?, and v= 1.37 billion km3. I need help in finding how to find m

 

[cindareally]

Also do I need to convert km3 to g/cm3? if so how do I go about doing that?

 

[gabby3306]

Global warming refers to the rise in average global temperature due to the increased concentration of certain gases, called greenhouse gases, in our atmosphere. Earth’s oceans, because of their high heat capacity, can absorb heat and therefore act to slow down global warming. How much heat would be required to warm Earth’s oceans by 1.0 °C? Assume that the volume of Earth’s oceans is 137 × 107 km3 and that the density of seawater is 1.03 g/cm3. Also assume that the heat capacity of seawater is the same as that of water.


Ok, so here is what I have and then I am lost. Can somebody please show me how to work this problem correctly. Thanks

D=M/V
D=1.03 g/(cm^2 )
V=1.37 billion km^3
M=1.03 G/(CM^2 )*1.37billionkm^3

 

[SteamKing]

Units! Units! Units!

How many grams in 1 KILOgram?

How many CENTImeters in 1 meter? (BTW, density has units of g/cm^3, not g/cm^2).

How many meters in 1 KILOmeter?

Remember, this is SI. It's superior to all other forms of measurement and so simple to use.

 

[Tsunoyukami]

Global warming refers to the rise in average global temperature due to the increased concentration of certain gases, called greenhouse gases, in our atmosphere. Earth’s oceans, because of their high heat capacity, can absorb heat and therefore act to slow down global warming. How much heat would be required to warm Earth’s oceans by 1.0 °C? Assume that the volume of Earth’s oceans is 137 × 107 km3 and that the density of seawater is 1.03 g/cm3. Also assume that the heat capacity of seawater is the same as that of water.


Ok, so here is what I have and then I am lost. Can somebody please show me how to work this problem correctly. Thanks

D=M/V
D=1.03 g/(cm^2 )
V=1.37 billion km^3
M=1.03 G/(CM^2 )*1.37billionkm^3

You need to pay attention to your units.

The easiest way to do this is to convert all measurements given to you in the problem statement into the most useful form for the question. What I mean by this, for example, is that the question involves the use of the heat capacity which is measured in (J/(gK), that is, Joules per Kelvin-gram. This means we would like to find the mass measured in grams to make it useful in the calculation of the change in heat.

When you're calculating the mass you must ensure that your units make sense. For example, as you know, D = M/V. If we want to compute M and we have D given in kg/m^{2} and V given in cm^{3} we can't simply write M = DV because the units of M "won't make sense" unless you convert either D or V to have similar units.

It does not matter whether or not you choose to convert to cm, m, or km. Try computing the mass after you have D and M in similar units.

Then, ask yourself: do I have an equation that tells me the amount of heat required to warm one gram of a substance by a single degree? (Hint: the answer should be yes).