Within the thermometer's range of operation, a given temperature difference will result in the same expansion in the column of the thermometric liquid.
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Well, darling, the limit of linearity range is the point at which a linear relationship between two variables breaks down. It's like when your favorite pair of shoes finally give out after miles of walking - they just can't keep up anymore. So, when you hit that limit, you better start looking for a new pair of kicks because things are about to get nonlinear real quick.
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